After defeating Grant in the Cyllage City Gym, you should continue north on Route 10: Menhir Trail.
Battle and Catch
In the grass and flowers, you can find Snubbull, Eevee, Hawlucha, Sigilyph, Emolga, Golett, Houndour (X only), and Electrike (Y only). You may also have horde encounters with Yanma, Nosepass, Houndour (X only) and Electrike (Y only).
Just north of where you entered Menhir Trail, there is an Iapapa Berry tree. North of the tree, there is a boulder that you can push with Strength. Go north after pushing the boulder and you will find a boulder puzzle. First, push the boulder down twice, then right three times. Then push it up twice, right three times, up once, and right until it falls into the hole. Get TM73 Thunder Wave to the right of where it fell.
Use your Dowsing Machine in the puzzle area to find a Revive in the bottom-left corner.
West of the Iapapa tree, you encounter Psychic Robert. He has a level 22 Solosis. Robert tells you that your pokémon's power levels are over 9000 (there's no way that can be right).
West of Psychic Robert, you find Tourist Fumiko running around. She has a level 19 Skiploom, a level 19 Dunsparce, and a level 19 Azumarill.
North of Tourist Fumiko, there is a field of large stones. At the bottom-right corner of this field, there is a Mind Plate.
North of the backpacker, there is a short wall of stones going across the middle of the field. In the northwest corner below this wall, you can get an X Accuracy. In the northeast corner, there is a hidden Paralyze Heal that you can find with the Dowsing Machine.
As you approach the gap in the low wall of stones, a Team Flare Grunt shows up and mentions a legend of 3000 years ago that explains something about the stones around you, but the grunt doesn't remember the rest. Then the Grunt battles you with a level 21 Houndour and a level 23 Golbat.
After that, the Grunt gets a message on the Holo Caster about the mission, then runs off.
North of the short wall, in the southeast corner, you can use your Dowsing Machine to find a Burn Heal.
North of the short wall, Psychic Sayid is to the left. He has a level 19 Meditite and a level 21 Kirlia.
North of Psychic Sayid, there is a Thunder Stone.
There is another short wall of stones to the north, with another Team Flare Grunt who battles you, this time with a level 23 Electrike and a level 21 Croagunk.
To the north, on the left, there is another Team Flare Grunt, this one with a level 24 Gulpin.
To the north, in the middle, you find Tourist Tomoko. She has a level 19 Drifloon, a level 19 Pachirisu, and a level 19 Hippopotas.
Go north through the stone arch to find yourself in Geosenge Town.