Teddiursa can only be found on Route 45 in Gold, while in Crystal it can only be found in both sides of Dark Cave during the morning. Be warned that it has a 50% chance to flee every turn.
In Gold, Ursaring is available on Route 28, Victory Road and Mt. Silver (exterior and interior), while in Crystal it's available in the Blackthorn side of Dark Cave during the morning and day and Mt. Silver's interior during the day.
"Bears are bad news" and with an Ursaring at your side, many of your opponents will be inclined to agree. While somewhat lacking in the coverage department, it can still tear through much of the competition through raw power alone.
Gym #1 - Falkner (Violet City, Flying-type): Teddiursa can easily Scratch out a victory against Pidgey, but taking on Pidgeotto will require some Potion support.
Gym #2 - Bugsy (Azalea Town, Bug-type): Metapod and Kakuna are just pathetic. Scyther, though, is able to build Fury Cutter up to lethal levels long before Teddiursa knocks it out. Use something more effective against it.
Rival (Azalea Town): Gastly can't hurt Teddiursa at all and Zubat is annoying but non-threatening. As for the starters, all are dangerous: Bayleef's Razor Leaf is too much to handle, Croconaw can tear through Teddiursa with Rage buildup and Quilava can lock Teddiursa down with SmokeScreen while gradually burning it to death.
Gym #3 - Whitney (Goldenrod City, Normal-type): Teddiursa's Return easily trounces Clefairy (barring it Metronoming something ridiculous like Cross Chop). Miltank's far too much a... well, tank, for Teddiursa to handle, though.
Rival (Burned Tower): Dig your way through Haunter and Magnemite, though beware of Curse from the former. Zubat's even easier now that Teddiursa has Return. Dig against Quilava to start, though switch to Return if it lands a Smokescreen. Croconaw will die from Return spam before it kills you. Bayleef is attemptable, but fall back if it gets Reflect up.
Gym #4 - Morty (Ecruteak City, Ghost-type): With Dig at its side, Teddiursa ain't afraid of no ghosts! Though be prepared to switch out on occasion, to clear up Curses and bring Awakenings for dealing with Gengar. Be sure to switch out of a Curse as early as you can too, because Morty's Pokémon love using Mean Look.
Eusine (Cianwood City, Crystal only): Two Returns will take out Drowzee, though make sure to keep Teddiursa awake as Dream Eater is seriously painful. Dig the Haunter; it can only harm you with Curse, which just makes your job easier. Stay away from Electrode - Thunder may be inaccurate, but it'll do quite a number if it hits.
Gym #5 - Chuck (Cianwood City, Fighting-type): Not unless you have a death wish.
Gym #6 - Jasmine (Olivine City, Steel-type): Dig makes quick work of the two Magnemite. Fire Punch, if you have a move slot to spare, is actually better for dealing with Steelix, though make sure to have a plan B, as Iron Tail does a large chunk of damage if it hits.
Rocket Executive battle #1 (Team Rocket HQ): If facing this at similar levels, avoid all SelfDestructers and be very cautious around the male executive's Raticate. If you've already beaten Jasmine though, this whole place is one big experience pinata.
Rocket Executive battle #2 (Team Rocket HQ): This is even easier. No bombs, and nothing that has particularly strong moves. Use Strength or Return against everything.
Gym #7 - Pryce (Mahogany Town, Ice-type): If you still have a Teddiursa, Seel's the only one it can really handle and even then its Rest can make it a bit of a pain. Ursaring, on the other hand, should have no trouble Returning its way through Seel and Dewgong while Piloswine is only a problem if it gets lucky with crits or freezing with Blizzard.
Rocket Executive battle #3 (Goldenrod Radio Tower): He has five Koffings and a Weezing and is a real problem; Ursaring can't take more than one SelfDestruct and won't survive Weezing's Explosion. Unless you feel like gambling with Dig-dodging, avoid.
Rival (Goldenrod Underground): The only Pokémon to worry about is Meganium (if he has it) and even then it'd have to get lucky with Razor Leaf crit or an early, long-lasting Reflect. Everything else falls swiftly to Dig (Magnemite and Haunter) or Return (all the rest).
Rocket Executive battle #4 (Goldenrod Radio Tower): The same battle as the HQ, but with an evolved Vileplume which still can't do much of anything. Normal STAB is the way to go.
Rocket Executive battle #5 (Goldenrod Radio Tower): Houndoom is kind of powerful with Faint Attack, but shouldn't be a real threat unless Ursaring is in low health. The other two are a non-issue, Koffing doesn't even have bomb moves.
Suicune (Bell Tower, Crystal only): Ursaring does surprisingly well here. Even Rain-boosted Bubblebeam will take 3 hits to defeat it and that's assuming Suicune's questionable AI can pull it off in the first place.
Gym #8 - Clair (Blackthorn City, Dragon-type): Individually, Ursaring can hand each Dragonair its butt with one or two Returns; taking them on collectively will require healing, particularly with all the paralysis flying around. Kingdra's another story: it's faster, and if it spams Surf you'll quickly find yourself short one Ursaring.
Rival (Victory Road): Sneasel is just...sad. Golbat won't survive more than two Returns at the most; mind the confusion though. Earthquake/Dig mows down Magneton and Haunter. Kadabra's down in one Return and Ursaring can easily tank a Psybeam. As for the starters, Earthquake/Return/Dig for Typhlosion and Return against Feraligatr and the same to Meganium, though if it gets Reflect up early be prepared to heal.
Elite Four Will (Indigo Plateau, Psychic-type): Return tears through the pair of Xatu and Jynx, though be mindful of status afflictions. Exeggutor's a bit bulkier and has Reflect on top of it; manageable, but probably not without healing. Slowbro's Curse might slow you down but not enough to make a difference, provided Reflect's not in play.
Elite Four Koga (Indigo Plateau, Poison-type): Return squashes Ariados and Venomoth like the bugs they are, though watch for the latter's Supersonic and Toxic. Fire Punch deals with Forretress - do not attempt without it, as Ursaring can't handle an Explosion. Earthquake Muk and Return Crobat, but X Accuracy is recommended for both, lest they avoid your attacks while whittling down your health with Toxic.
Elite Four Bruno (Indigo Plateau, Fighting-type): Hitmontop lacks STAB and has weak attacks, so go ahead. Though it's best to stick to Earthquake for it in order to hit it while it's Digging. Avoid Hitmonlee, Hitmonchan and Machamp as Fighting moves make Ursaring a sad grizzly. Earthquake's fine for dispatching Onix, though if you have Ice Punch it'd be even better.
Elite Four Karen (Indigo Plateau, Dark-type): Use an X Accuracy for dealing with Umbreon's Sand-Attack as even the mighty Ursaring will take a few Returns to break through its bulk. Vileplume's not particularly difficult, albeit annoying if it lands Stun Spore. Gengar can't hurt you directly, but Destiny Bond is a thing, so its probably better to use someone else. Murkrow's frail and not that impressive on the offense either- Return it like it was nothing. Earthquake slaughters Houndoom, possibly even one-shotting it, though only face it if healthy as Flamethrower dishes out massive amounts of damage.
Champion Lance (Indigo Plateau, Flying-type): Gyarados, the three Dragonite and Charizard should go down in 2-3 Returns each, though only with a regular infusion of Full Restores; luckily Lance is overly fond of Hyper Beam, giving you lots of free turns to work with. Aerodactyl's better off avoided as it resists or is immune to your best moves.
From this point onwards, you can fight the gyms in any order, though you will need to retrieve the Machine Parts from the Cerulean City gym before you have access to the earlier portion of Kanto. Feel free to anticipate or postpone any battles as needed.
Gym #9 - Brock (Pewter City, Rock-type): It's an Earthquake party and Brock's whole team is invited! Ursaring should have no trouble at all here.
Rival (Mt. Moon, optional): Mostly the same as last time. About the only differences of note are that Kadabra is now an Alakazam with Psychic, which could pose problems if your health is low, and Meganium's swapped Reflect for Light Screen, making it even easier to beat.
Gym #10 - Misty (Cerulean City, Water-type): Return works wonders on everything here, though Lapras' bulk and Starmie's Speed means they'll likely each get a hit off first.
Gym #11 - Lt. Surge (Vermilion City, Electric-type): Earthquake massacres his entire team. Be prepared to heal though, as everything is faster than you, and be especially wary around the two Electrode as they both have Explosion. X Accuracy might also be desired, as three of his Pokémon have Double Team.
Gym #12 - Erika (Celadon City, Grass-type): Given how her team has poor damage output, surprisingly few status afflictions and (apart from Jumpluff) are rather slow, Ursaring should have no trouble Return-spamming its way to victory.
Gym #13 - Janine (Fuchsia City, Poison-type): Oh, Janine! You and your ridiculous amount of underleveledness! Put her out of her misery with Earthquake for the Weezing pair and Return for everything else. The only possible threat is Crobat using Confuse Ray, but that's what Bitter Berries are for.
Gym #14 - Sabrina (Saffron City, Psychic-type): Espeon and Mr. Mime should pose little trouble apart from Sand-Attack irritation from the former. Alakazam's significantly more problematic; if it gets Reflect up it'll be able to survive a Return and counter with a devastating Psychic.
Gym #15 - Blaine (Seafoam Islands, Fire-type): Earthquake, Earthquake, Earthquake. The only way he could kill Ursaring is if Rapidash nails a crit Fire Blast while Sunny Day is in effect. (If that does happen, feel free to scream all the four-letter words you know at the RNG.)
Gym #16 - Blue (Viridian City): Pidgeot's attacks are sad; Return it to death, or use it to Curse spam if you feel evil. Alakazam has Reflect, and while this probably won't help it (given the AI's persistence in using Recover), it'll make dealing with the rest of his team harder if you haven't Cursed. Rhydon's better handled with a Water or Grass-type due to its extreme Defense. Don't fight Gyarados if Reflect is still active or if it uses Rain Dance; otherwise, though, it should be manageable. Exeggutor will probably require healing due to SolarBeam hitting very hard, and it is recommended to stay out of the fight altogether if it uses Sunny Day. Avoid Arcanine if the sun's up, or if Ursaring's too low on health to tank an Extremespeed; if neither applies, Earthquake away.
Rival (Indigo Plateau, optional): Very much like the Mt. Moon fight, though note that Alakazam's picked up Reflect, making it and whatever Pokémon come after it that much more dangerous.
Red (Mt. Silver): Pikachu's glassiness won't stand up to an Earthquake, and again, it can be used for Curse setups. Return spam will shut down Espeon, but if it gets Reflect up, Ursaring will be in serious trouble without the aforementioned Curse boosts. Snorlax is doable, but with it having Rest it could be a test of patience and PP (again, not a problem with Curses). Venusaur's a similar story, especially if it activates Sunny Day to boost its Synthesis. Charizard has too much literal fire power for comfort; even moreso if the sun's up. Blastoise is too powerful in rain or if weatherless, but sunlight brings it down to manageable levels.
Teddiursa starts with Scratch and Leer; basic, but Teddiursa's tough enough to make it work. At level 8 it learns Lick; not something for the long run, but at least it lets it fight Gastlys. At level 15 it learns Fury Swipes; on average more powerful than Scratch, but 80% accuracy's a bit unfortunate. At level 22 it learns Faint Attack, unfortunately it's special and therefore not that useful. At level 29 it learns Rest; keep it if you want to play with Sleep Talk (which is actually viable in this gen) but otherwise healing items are generally more efficient. At level 39 it learns Slash, but you should have Return by now. At level 49 it learns Snore, but if you're using a Rest set you're much better off with Sleep Talk. Finally, at level 59 it learns Thrash, but why would you want to use a move weaker than Return that locks you into battle to boot?
Among TMs, Ursaring fares well enough. Return is the major one; STAB Return off of 130 Attack can wreck plenty of face by itself. Dig and later Earthquake deals with the Gastly line and pesky Rock-types, among other things. Curse will help out with its mediocre Defense and it's not like Ursaring will miss the Speed. (Plus, who doesn't love more power?) Ursaring can also learn the elemental punches; Fire Punch is recommended for high Defense Steel-types and/or Ice Punch for high Defense Rock/Ground types. Lastly, Sleep Talk is a possibility; in this gen, if Rest is called, it will restore health, making Resttalking a bit less of a gamble.
Standard: Return, Earthquake, and any two between Curse / Ice Punch / Fire Punch