Graveler can be found as early as Route 13 in the breakable rocks. It can also be found in Route 18, Terminus Cave, and Victory Road. Geodude can be found in the above places sans Route 13.
Geodude skipped Gen V, which is a shame. Because in that gen, Sturdy got a huge buff that made it a instant Focus Sash at full health. Meaning Geodude as it is slow, can take a super effective hit and launch back a super effective hit with little worries. This added onto the usefulness that Gen IV provided with more powerful moves, which is all it needs. Geodude ages like a fine wine here, but one should be wary of its many common weaknesses, especially due to the resurgence of Steel types.
It should be noted that Geodude's Hidden Ability Sand Veil is available only if the player is lucky to find one in a horde battle in Victory Road. This ability should only be used in conjunction with Sandstorm set up, but Sturdy is much better.
It is recommended that if the player cannot evolve Graveler into Golem for any reason, that it hold the Eviolite.
Gym #5 - Clemont (Lumiose City, Electric-type): Emolga is easy with Rock STAB, but it is likely to break Graveler/Golem's Sturdy. Which is a problem, Magneton and Heliolisk can OHKO with Mirror Shot and Grass Knot. Magneton even has Sturdy as a liability. This is a shame, as Graveler/Golem can OHKO both with Earthquake normally. If Graveler/Golem is taught Rock Polish via TM, it can set up on Emolga and heal up, to handle the other two much easier.
Rival (Route 14): Absol is the only safe kill for Graveler/Golem, avoid Meowstic and the starter.
Gym #6 - Valerie (Laverre City, Fairy-type): Mawile can be defeated easily, as its only offensive moves are Dark-typed. Graveler/Golem can set up Rock Polish here, and take out Mr. Mime with ease who otherwise would be a threat. However, Sylveon will be a struggle.
Celosia and Bryony (Poké Ball Factory, tag battle with rival): Graveler/Golem wrecks both, especially if it has Earthquake.
Mable (Frost Cavern): Houndoom is all physical, meaning Graveler/Golem can live and kill it with Earthquake.
Rival (Anistar City): Same as the last one, plus a Kanto Eeveeloution dependent on the starter. Flareon and Jolteon are ok, Vaporeon is not. Reminder that Rock Polish is an option, to deal with Greninja and Delphox easier.
Gym #7 - Olympia (Anistar City, Psychic-type): The future is dark for Graveler/Golem here.
Lysandre battle #1 (Lysandre Labs): If Graveler/Golem knows Protect, it can try to protect itself from Mienfoo's High Jump Kick. Otherwise, don't face it head on. Murkrow will hurt with Steel Wing, but Graveler/Golem can live at full health and kill with Rock STAB. Pyroar can't 2HKO with anything at full health and Eviolite, so hit back with Earthquake. Gyarados has three super effective moves, thus it should be avoided like the plague.
Aliana (Lysandre Labs): Mightyena can be fought, but Druddigon has Surf and thus is a bad matchup. Someone else should handle her, specifically a Special Attacker.
Celosia (Lysandre Labs): Earthquake takes care of both Manectric and Drapion.
Bryony (Lysandre Labs): Set up Power Up Punch on Liepard, that will give Graveler/Golem enough umph to kill Bisharp in one hit. It can take at least one non-crit Iron Head.
Mable (Lysandre Labs): Graveler/Golem can take any of Houndoom's attacks and launch back with Earthquake. However with the damage taken, it might be a bit tricky in taking down Weavile with Brick Break or Rock STAB.
Xerosic (Lysandre Labs): Graveler/Golem kills Crobat easily with Rock STAB, despite Steel Wing. However, Malamar will get dangerous with Contrary Superpower bulking it up. Not even Steamroller can kill it fast enough. Graveler/Golem should switch to someone who can kill Malamar quickly. A creative yet risky strategy is to set up Rock Polish on Crobat to build speed, then hope Steamroller flinches Malamar to score another free hit.
Lysandre battle #2 (Team Flare Secret HQ): Mienshao should only be handled if Graveler/Golem can weaken it with Protect, however not even Eviolite Graveler can handle High Jump Kick. Honchkrow will hurt more with Steel Wing, but Graveler/Golem can edge out with good health and Rock STAB. Pyroar is the same as last time, OHKO'd by Earthquake. Gyarados should again not be fought at all. Graveler/Golem's best role in this fight is to set up Stealth Rock against Mienshao; so that Honchkrow, Pyroar, and Gyarados can all be weakened substantially for the other teammate.
Xerneas (Team Flare Secret HQ, X only): Geomancy means no.
Yveltal (Team Flare Secret HQ, Y only): Graveler/Golem cannot survive Dark Aura-boosted STAB Dark Pulse.
Lysandre battle #3 (Team Flare Secret HQ): The strategy of setting up Stealth Rock against Mienshao so that the other three Pokemon especially Gyarados pre-Mega take damage is a valid one, especially since it helps the incoming teammate clean up the mess.
Professor Sycamore (Couriway Town): Charizard yes, other two no.
Shauna (Route 19): Graveler/Golem can take out Delcatty, preferably with Power Up Punch. Goodra and the starter are too dangerous, unless you set up Rock Polish on Delcatty and still have enough attack to handle the last two.
Tierno (Route 19): Talonflame is the only safe kill, obviously.
Trevor (Route 19): Raichu is handled with Earthquake and Aerodactyl with Rock STAB. Florges has Energy Ball and Moonblast, so don't try.
Gym #8 - Wulfric (Snowbelle City, Ice-type): Yeah, Wulfric leads with Abomasnow which has Energy Ball and insta-Hail which wrecks Sturdy. Don't have Graveler/Golem fight in this match, or suffer a defeat more humiliating than Ash's.
Rival (Victory Road): Altaria is new, and can only be killed by prior setup as it can kill Graveler/Golem with its special attacks.
Elite Four Wikstrom (Pokémon League, Ironworks Chamber, Steel-type): This is not a good matchup for Graveler/Golem, due to the type disadvantage. Klefki will kill with Flash Cannon from the start. Probopass is slightly slower than Golem only, but it also has Sturdy. Although Golem will likely not OHKO with Earthquake, making this moot and in Golem's favor just barely. Scizor runs Bullet Punch, the bane of Sturdy Graveler/Golem. Aegislash should only be fought at full health, so that it can change to Stance Mode and while Graveler/Golem survive a hit with Sturdy, it can retaliate on Aegislash's paper-thin defenses with Earthquake. Earthquake also is not affected by King's Shield's Attack drop either.
Elite Four Malva (Pokémon League, Blazing Chamber, Fire-type): Pyroar is handled easily with Earthquake, although Noble Roar can be a pain. Against Torkoal, Graveler/Golem outspeeds and only has to worry about Curse + Earthquake. Thus, it should kill it quickly. Chandelure can kill with Shadow Ball, but will die to a Earthquake easily. Talonflame, is a joke to Rock STAB. It is advised that Graveler/Golem set up Rock Polish and/or Stealth Rock to make the match easier. Also it's funny to see Talonflame come into Stealth Rock, ahh Smogon...
Elite Four Drasna (Pokémon League, Dragonmark Chamber, Dragon-type): Golem has a SLIGHT chance to outspeed Dragalge, which is something as it has Surf. Earthquake is a guaranteed OHKO, and Golem will still have full health for the next opponent. Although, Druddigon has Revenge and Dragon Tail to mess with Graveler/Golem. This would probably be the best time to set up Stealth Rock. Altaria is not a good matchup due to Moonblast and Dragon Pulse, but Graveler/Golem has a chance to make good damage and OHKO with Stone Edge after Stealth Rock. Although Altaria can use Cotton Guard to take Rock STAB or Sing to put Graveler/Golem away. The same is said for Noivern, who plays almost the same as Altaria without the annoyance of defense boosts and singing. In a defensive aspect, Graveler/Golem should switch out after setting up Stealth Rock on Druddigon if possible, so that the next teammate who can handle the rest has an easier time.
Elite Four Siebold (Pokémon League, Flood Chamber, Water-type): It is unadvised to cook a Rock, but Siebold will damn try and will do a good job at it.
Champion Diantha (Pokémon League, Radiant Chamber): This matchup is 'on the rocks'. In the front, Hawlucha knows Flying Press to mess with it. Tyrantrum has Earthquake, though Graveler/Golem can survive to kill it with its own STAB Earthquake. Aurorus has Blizzard, an ultimate no for Graveler/Golem. Plus, Screens are annoying. Gourgeist resists Earthquake, and has bulk for neutral (Rock) hits. It also has Seed Bomb, to quickly dispose of Graveler/Golem. Goodra has Muddy Water and Focus Blast in its arsenal, so don't bother. Mega Gardevoir is overkill, seriously. As Golem, it has one niche in this battle. It should be preserved until the fight against Mega Gardevoir, where it can take any hit (presuming it has Sturdy), and launch back with Heavy Slam, bringing in the OHKO.
Post-Game: Against AZ, Graveler/Golem has only Torkoal to safely defeat. As for the Looker Sidequest, use Graveler/Golem only where the matchup is in its favor.
Graveler's earliest appearance has it around level 26-28, where it starts off with Rollout, Magnitude, Rock Throw, Rock Blast, or Smack Down (level 27+) replacing Rollout. Rollout isn't essential and useless without Defense Curl. Magnitude will be the go-to Ground move until Earthquake later on. Rock Throw and Rock Blast are the primary Rock STAB choices for now. At level 31, Self Destruct is not a valid choice if Graveler/Golem wants to keep living. Bulldoze at level 36 while it has the niche of lowering speed, isn't so good considering Graveler/Golem already has abysmal speed to begin with. Stealth Rock at level 42 is a blessing, giving Graveler/Golem a defensive edge against full teams rather than just one Pokemon. Earthquake finally comes at level 47, the staple Ground STAB. Explosion at level 53 is another joke move, moving on. If you somehow had the unfortunate fate of getting Rock Head as an ability, Double-Edge can be paired with that. Stone-Edge is the reward at level 64, around the Elite Four and the best Rock STAB Graveler/Golem can get.
Golem has two secret moves that its pre-evos don't get, Steamroller and Heavy Slam. Steamroller is good against Grass, Psychic, and Dark. Which is, actually more utility than Brick Break. Though it is very low power compared to most of Golem's stronger attacks. It is only good for the flinch chance. Heavy Slam is very good as Golem is one of the heaviest non-legendary Pokemon, thus taking advantage of its high base power.
TM wise, Stone-Edge can be earned just after the Flare arc and is an earlier way of getting the move. Sandstorm is a good fit for the Sand Veil variants, but that's pretty much it. Brick Break vs. Power Up Punch is based on preference, but both are solid fighting moves. Rock Tomb is much better than Rock Throw especially with the speed drop, meaning Graveler/Golem can ditch it on the go. Rock Polish is relatively early and essential if Graveler/Golem wants to outspeed, giving it more chances to OHKO rather than be OHKO'd. On the contrary, Gyro Ball is nice if Graveler/Golem wants to act slow, but Heavy Slam is simply better. Rock Slide is stronger than Rock Tomb but has 5 less accuracy, it also has a flinch chance that a normal Graveler/Golem can't utilize as it is really slow. Though a Rock Polish set can try to abuse it.
Physical: Stone Edge, Earthquake, Power Up Punch/Stealth Rock, Heavy Slam/Double-Edge
Speedy: Rock Polish, Rock Slide/Rock Tomb, Steamroller/Heavy Slam, Earthquake
Minimum stats are calculated with 0 EVs, IVs of 0, and a hindering nature, if applicable.
Maximum stats are calculated with 252 EVs, IVs of 31, and a helpful nature, if applicable.
Geodude Line Rankings
What Nature do I want? If you want to take advantage of Rock Polish, then Jolly is the best way to go. Otherwise, Brave or Adamant are also good to use.
What Ability do I want? Sturdy, no question. Rock Head has no use outside of Double-Edge.
At what point in the game should I be evolved? You will most likely catch it as a Graveler either pre-Clemont or around Couriway Town. You should evolve it as soon as possible, or hand it the Eviolite.
How good is the Geodude line in a Nuzlocke? Though not as good thanks to more diverse movesets of other Pokemon, Geodude holds it own defensively and offensively thanks to Sturdy. It has lost a bit of luster from the Johto age, but it is still a unique asset.
Weaknesses: Water (4x), Grass (4x), Fighting, Ice, Steel, Ground
Resistances: Fire, Rock, Flying, Bug, Poison, Normal