After you get TMs, a Pokétch app, and battle trainers in Oreburgh Gate, you go east to reach Oreburgh City.
Go to the Gym
The kid at the entrance of town takes you to the Oreburgh City Gym. Your friend is at the door. He tells you that the Oreburgh City Gym Leader went to the Oreburgh Mine, so you can't challenge him yet.
In the building to the left of the Poké Mart, there is a kid on the ground floor who will trade you her Abra (named Kazza) for a Machop. Her Abra is holding an Oran Berry. If you don't have a Machop, be sure to come back later if you get one. Traded pokémon level up more quickly.
Show a Pokémon
In the same building, someone on the top floor asks to see a Zubat. If you have one, you get a free a Heal Ball.
Get a Dusk Ball
In the other northwest building, a lass on the upper floor will give you a Dusk Ball. Use a Dusk Ball in a cave or at night for a better chance of catching a pokémon.
Get a Great Ball
In a building in the east part of Oreburgh City, talk to the kid on the upper floor to get a Great Ball. It has a higher chance of catching pokémon than a regular Poké Ball.
If you go northeast from Oreburgh City, you will enter Route 207. You can't go very far, but there is a Poké Ball in the northwest part of the area that you can access, and a hidden Poké Ball in the corner east of that.
In the grass in Route 207, you can catch Geodude, Kricketot, Machop, and (only at night) Zubat.
Get a Super Potion
Go south from the Pokémon Center and go to the southeast of the area. Talk to the miner there to get a Super Potion.
Go to the Mine
Directly south from the Oreburgh Pokémon Center, you will find the Oreburgh Coal Mine.