What would you like to see in X/Y Sequels?

I would really like move tutors although I feel like its safe to say they will have them. Emerald, Platinum, and Black 2/White 2 all had them.

 

I want a facility that lets you use rental Pokémon. I miss Battle Factory.

 

The Battle Facilities should make a return, but they should still keep the Battle Maison. They should probably extend on the Looker Missions, since it does imply that there will be more but not with that character. Also, something more important with Zygarde through the game, since it seems to be important according to its Pokédex entry and it is the thiird part of the trio.

Also, there should be mega stones that are only found in the next games, like maybe megas for the Jhoto starters and Pokémon who didn't get a mega in these games.

 

Pretty much what RedScizor said; move tutors would be awesome to have especially with the new Pokémon. Also what Sachi said too.
Now things I want, I guess a storyline without Team Flare involved. In B2W2, we had a Team Plasma revival and it was pretty generic I guess. I think something like the fall of Team Flare and a new team tries to take over the Kalos region can sound interesting. Additionally, I would like to see Pokémon learn better moves such as Head Smash and Brave Bird Aerodactyl (to abuse Rock Head better).
This sounds unpopular but the underground was pretty cool; can use it to farm shards and gems.

 

More backstory for the Fab Five--sure, Shauna got some sweet moments, and Trevor gets a little character development, but Tierno didn't really stand out--what motivated him to love dancing?

Incorporate this into a Contest-esque mini game (The PR videos were a bit lame)

Get the story going a little bit faster--the story never went anywhere until late in the game when you stopped Team Flare

Move the battle with Az until after you stop Team Flare or in the post game--making it part of the ending just felt odd

 

A challenge mode, and Elite 4 that grow in strength after you beat them the first time. The overall lack of difficulty and no options to add any is one of the few things I don't like much about X and Y.

 

More story, maybe because the legendaries were caught the world is out of balance hence the third legendary wreaking havoc on the world. Battle frontier would be nice like most people have said. More megas, the other starters deserve them since blaziken got one when his hoenn fellows didn't. And maybe make the game a little harder...the gym leaders were kind of weak I never struggled with any of them.

 

Move tutors, better post-game content, better storyline (Don't get me wrong I think XY's plot was quite interesting but it's a bit lacking in character development...)
And I think there should be more Mega Pokémon. Why did Blaziken get one but Swampert and Sceptile didn't? Sableye should get one too imo

 

Multiple save files? *sigh* That's not going to happen anyway...

But yeah, more post-game. I'm at the point in X&Y where I have nothing else to do besides collecting every single Pokémon (breeding, grinding, evolving, box, and repeat)
I wouldn't say better storyline, but more unique. Whether it is with unexpected plot-twist, or multiple endings depending on your performance, it would add a lot of replayability.
But on the other hand, I'd like to see some more freedom (I hate it when you can't explore the region a bit further because you need to do this little part of the storyline)
And don't make a crap ton of characters, all with just little personality (really, Serena, Shauna, Tierno and Trevor?)

Overall, don't make the game more difficult, but wider. More possibilities means more replayability means more fun.