After you make your way through Chargestone Cave, you arrive in Mistralton City.
Meet Professor Juniper
Go to the north part of town to finally meet Professor Juniper. She gives you a Master Ball, which has a 100% catch rate. You will probably only ever get one of these, so be sure to save it and use it on a legendary.
Skyla arrives and says you can go to Celestial Tower to train, or just battle her at the gym.
You can get quite a few items in the airport. Talk to the woman near the entrance to get a Sharp Beak. If you have a Flying or Psychic pokemon, talk to the person in the top-right to get a Net Ball.
Explore the runway to get TM58 Sky Drop, a Flying Gem and a Max Repel. You can also unlock a Funfest Mission and find a guy who wants to buy Mulch.
The woman in the house next to the Pokémon Center will give you items depending on how many TMs you have found. You can also get an Iron from her trash can.
You can buy some TMs in the Pokémon Center.
If you want to go to the Celestial Tower before the Mistralton Gym, go northeast to Route 7.