After finishing X or Y you can go to...
Vaniville Town
After the credits roll, start your game back up to find yourself back in Vaniville Town. Your mother will tell you Professor Sycamore wishes to see you at the Lumiose Station at North Boulevard.Right outside your home is Shauna. She will offer you the first evolution of her own Starter Pokemon. The Pokemon you get depends on the Pokemon you chose at the start of the game. It will always be at Level 5.
Your Starter Chespin Fennekin Froakie
Shauna's Starter Froakie Chespin Fennekin
Nature Jolly Adamant Modest
Before going to meet Professor Sycamore, you can catch three Legendary Pokemon at three locations. Two are stationary, and the third will be roaming before going stationary. You don't have to go now if you don't want to.
Zygarde is located inside Terminus Cave.
Mewtwo is located in Unknown Dungeon.
Articuno, Zapdos, or Moltres will be roaming around select routes. Articuno will appear if you chose Chespin, Zapdos if you chose Fennekin, and Moltres if you chose Froakie. After encountering them ten times, they will go to Sea Spirit's Den.
- Lumiose City
There are a number of things to do in Lumiose City after becoming the Kalos Champion. Here's a quick checklist on where to go and what to do.
The first thing you should do is head to the second floor of the Sycamore Pokemon Lab. Speak to one of the assistants to obtain the Pokemon Radar. Use this to chain Shiny Pokemon, or to capture Pokemon of the same species.
Talk to Diantha in Cafe Soleil. She will offer you a level 5 Modest Ralts that is holding Gardevoirite. You can trade any Pokemon to get this Ralts.
You can now test your skills at the Battle Institute in the North Bouleavard, or eat and battle at Restaurant Le Wow.
When ready to progress the main story, head to Lumiose Station. When you enter, you'll find Sina and Dexio. They will upgrade your Pokedex one last time to the National Pokedex. This shows all 700+ Pokemon! Talk to Professor Sycamore up ahead to get the TMV Pass. This allows you to take the train from Lumiose City to Kiloude City.
Kiloude City is the final city in Kalos. After reaching it, you can use Fly to quickly travel back and forth, or just use the train from Lumiose City.
The main reason for coming to Kiloude is to try out the Battle Maison and to face your Rival one last time. After defeating your Rival, he/she will tell you Professor Sycamore wants to speak to you in Anistar City
Speak to the girl in this station to receive a Pokedex Quiz. The answer should be "Threads" (X Version) or "Perfume" (Y Version). Your reward for answering right will be one Max Revive.
Exit the station and you'll receive the Vs. Recorder from a man. This allows you to save select Pokemon Battles in video form and upload them if you want.
Walk east to find the Pokemon Center passed the first house. Inside the Pokemon Center is a man who can analyze the Individual Values of your Pokemon, sort of like the Characteristics in each Pokemon's summary.
The left Poke Mart has the usual stuff, but the right Poke Mart has a number of Technical Machines.
Inside the house to the east of the Pokemon Center is a girl who will give you TM91 Flash Cannon just for speaking to her.
Exit the house and go northeast to find a Nugget outside.
The Battle Maison is a Battle Facility in the middle of Kiloude City. You can battle tough trainers and earn Battle Points. Exchange these points for some very rare and useful Items. Fight at least one match in the Battle Maison to progress the main storyline.
Visit the house to the west of the Battle Maison to find a man in need of some advice. He will ask three questions about battling, and there are no wrong answers. After the questions, he will challenge you to a Pokemon Battle.
Ace Trainer Anton
Reward: 6,600 Pokédollars
Weezing 
Moves:
Sludge Bomb
Dark Pulse
Shadow Ball
Protect
Eelektross 
Moves:
Gastro Acid
Thunderbolt
Flamethrower
Flash Cannon
Bronzong 
Moves:
Psychic
Block
Gravity
- At the very northwest part of Kiloude City is a woman who is looking for inspiration for her art. If you are wearing a colorful outfit (you can tell if there is a splash of colors behind your character when it asks you to confirm the customization), she will thank you for giving her inspiration. She will reward you with a Pangoro hat if you play as the male trainer, or the Sundae dress that looks like a Slurpuff if you play as the female trainer.
Fly over to Anistar City and go over to the Sun Dial in the west. Here you will find Professor Sycamore. He'll tell you what his research has found regarding Mega Stones and the Mega Ring. Touch the Sun Dial Crystal to power up your Mega Ring. This will allow you to find more Mega Stones around Kalos between 8 PM and 9 PM.
The final part of the main storyline will happen after powering up your Mega Ring. Head to Lumiose City to get a mysterious call. You will need to travel to the new Looker Bureau in Rouge Plaza. See the Looker Bureau page for a full walkthrough of this final mission.
Clearing this mission will allow you to eat at Sushi High Roller.
Hope I helped!!
