Pokemon X and Y Walkthrough - Anistar City
Sina is waiting by the benches to give you some Repeat Balls. They're stronger against types of Pokemon you've already caught. The girl standing outside the Pokemon Center can read your Pokemons' memories. It's not very useful, but it can be fun to recall some of the things you've done on your journey together so far.
Mr. Bonding is waiting inside the Pokemon Center to give you the Exp. Point O-Power. There's also a Hex Maniac that gives away one of four TMs depending on the time of day: TM 32 Double Team, TM 35 Flamethrower, TM 77 Psych Up, or TM 90 Substitute.
A Psychic inside the house east of the Pokemon Center gives away TM 10 Hidden Power. This move's type is based on the hidden stats of the Pokemon that learns it. This way you can have a Pokemon learn a type of move it normally can't. Fortunately, the same guy can tell you what type any Pokemon's Hidden Power will be.
The house north of the boutique is where you can find the old man that knows about the legendary Pokemon. The house north of his has a unique side quest. The eldery man inside asks to watch over one of your Pokemon that's level 5 or less. If you let him watch it for a while and come back, there will only be a Poke Ball on the floor with a note. The note alludes to the man's death and has a Comet Shard attached. That's pretty dark for a Pokemon game, but at least you made the man happy in his final days.
Continue north to the city's gym. Your rival will stop you for a battle as promised.
Other than taking a look at the sun dial, that's everything in the city. Enter the gym when you're ready.