Um, you can do the following:
- Looker Bureau
- Battle Maison and Friend Safari
- Trade for other starter Pokemon in Vaniville town
- Get the Pokeradar
- Catch Mewtwo, Zygarde, and the legendary bird trio
- Get and complete the National Dex
- Upgrade your Mega Ring in Anistar City
- Receive a Pancham hat or a Sundae Dress(depending on Gender) In Kiloude City
- Fill up the Pokedex
- Trade on the GTS
- Battle your rival in Kiloude City
- Breed and train
- Challenge the League again
- Get the Shiny charm for completing the National Dex
- Transfer Pokemon to PokeBank
- Collect all the Mega stones
- Get event Pokemon
- Get Heart scale from Tierno
- Battle Chateau
- Go fishing
- Horde training
- Wonder trade Magikarp
- Restaurant's in Lumiose City
- Get more money
- Get all the TMs
- Make trainer videos in Lumiose City
- Trade with Diantha
- Grow berries
- Go shopping
- Get the Oval charm after completing the Kalos Pokedex
Source and My Experience
That's mostly it for Pokemon Y or X[and this has been asked already]
-Axel71,my last answer with this username
