Pokemon X and Y Walkthrough: Shalour City
Enter the Pokemon Center to find Mr. Bonding staring at a wall. He gives the Critical Power O-Power. The Poke Mart has a few TMs for sale that you might find useful. Sandstorm and Hail are both attacks that affect the weather to deal small amounts of damage in between turns to Pokemon that don't share the move's type.
The house east of the Pokemon Center has a Scientist inside that checks your Pokedex. If you've seen enough Pokemon from Coastal Kalos, he gives you an Eviolite. For reference, I had seen 41 Pokemon at this point. When held, an Eviolite increases the Defense and Special Defense of a Pokemon that isn't fully evolved.
The first house west of the Pokemon Center has an old lady inside that gives a Soothe Bell. It doubles the happiness a Pokemon earns. The other house has a Rising Star that gives a Footprint Ribbon to Pokemon that you've raised yourself. There's also a woman in this house looking for a Flying or Psychic-type Pokemon to help reach her luggage. If you have one, she gives some Stardusts. They can be sold for a high price.
Tierno and Trevor stop you as you take the path north of the Pokemon Center. They remind you to visit the Mega Evolution guru at the Tower of Mastery. A Psychic inside the house next to the gym will trade berries. The gym is currently closed because Korrina is training at the Tower of Mastery. That means one thing...you should go to the Tower of Mastery at the north end of town. On your way there, Tierno gives you an Intriguing Stone on the beach. Pick up the Max Ether near the tower's outer brick wall and then enter the tower.