After finding out that Team Magma/Aqua has kidnapped Professor Cozmo, you go to Route 114 on your way to Meteor Falls.
Visit the Fossil Maniac's House
Go west from Fallarbor Town and you will find the Fossil Maniac's House. Talk to the kid standing near the door to receive TM28 Dig. This move is a Ground-type attack in battle, and it can be used outside of battle in caves or dungeons to go back to the entrance, just like an Escape Rope.
If you wish, you can go into the door that the kid is standing near. You will find the Fossil Maniac in the back of the tunnel.
Get Another TM
Go southwest from the Fossil Maniac's house and talk to the guy there to get TM05 Roar.
Explore the Route
If you use the Old Rod in this route, you can find Goldeen and Magikarp. In the grass in this route (south of the water), you can find Zangoose (in Omega Ruby) or Seviper (in Alpha Sapphire), Nuzleaf (in Omega Ruby) or Lombre (in Alpha Sapphire), Surskit, and Swablu.
Go south and you find Fisherman Claude, who has Corphish and Wailmer.
South of there is Fisherman Nolan, who has a Gyarados.
After the bridge, use the Dowsing Machine and go west to find a hidden Revive on some flowers.
Go east from the bridge and you will find Lanette's house. Talk to her to get a doll for your base. If you are playing Omega Ruby, she gives you a Seedot Doll. If you are playing Alpha Sapphire, she gives you a Lotad Doll. Then talk to her again and say yes if you want her move the "Organize Boxes" button to the top of the list of buttons when you open Lanette's PC. You can always talk to her again to turn it off.
Talk to the guy south of Lanette's House to get a random berry.
There are some Aspear berry trees southeast of Lanette's House.
Southwest of Lanette's house, you find Teammates Tyra & Ivy, who challenge you to a double battle with Roselia and Azumarill.
Use the Dowsing Machine and go southeast from the Teammates to find a hidden Carbos.
Southwest of the Teammates, you find Poké Maniac Steve, who has an Aron.
Go up the stairs near the Poké Maniac. There is a Secret Spot nearby that you can use Secret Power on to open up a new Secret Base.
North of there, if you have a pokémon with you that knows Rock Smash, use it on the rock to the north to reach a Protein.
Go southwest. You will see your neighbor run after Team Magma/Aqua.
Go south and you will find Camper Shane, who has Minun and Volbeat.
Use the Dowsing Machine and look in the nearby crater to find a hidden Comet Shard.
Then use the Dowsing Machine in the next crater to find a hidden Rare Bone.
Go east and walk up the narrow path north of the big crater to get an Energy Powder.
Go south and then up the stairs. North of the stairs, there are some rocks that you can smash with Rock Smash to reach the Secret Spot in the wall. Use Secret Power there if you want to start a Secret Base there.
To the east, there is another Secret Spot.
To the south, Kindler Bernie is running around. He has Slugma and Wingull.
Go south from Bernie and you will find Hiker Lucas, who has two Geodudes.
Go up the stairs near the Hiker. Go west across the crater and you will find Hiker Lenny, who has Machop.
Go south from Lenny. There are a couple more Secret Spots: one to the south and one to the north of the stairs.
Go west to find the entrance to Meteor Falls.