Pokemon X and Y Walkthrough - Coumarine City
Coumarine City is broken up into two different areas, north and south. You can travel between them using the Seaside Station monorail. Let's start by exploring the north side.
Your rival sends a message on the Holo Caster telling you to prepare for a battle in front of the city's gym. The old man in the first house gives a Silk Scarf, which boosts the damage of Normal-type moves. The stand sells Incense, which is needed to make certain baby Pokemon eggs. For example, a female Snorlax holding a Full Incense will produce a Munchlax egg. The Fisherman by the stand gives away a Good Rod.
The blonde-haired girl on the first floor of the Coumarine Hotel will give you a Lucky Egg if you show her a Pokemon with a high friendship level. If you've trained a Pokemon for a while without letting it faint too much, it should be enough to get the prize. The Lucky Egg makes the holder gain 50% more experience than normal. The woman on the second floor gives away a Smile Ribbon. Finally, the boy in the last room of the second floor is the game director. If you manage to catch all 718 Pokemon he will give you a certificate. Good luck.
The girl overlooking the ocean west of the hotel has a daily quiz. If you answer correctly, she gives you the TM of the question asked. The four TMs are Confide, Acrobatics, Embargo, and Trick Room. Even if you answer incorrectly she gives you an unlimited number of guesses. Keep coming back every day until you win all four TMs. Acrobatics is especially useful in the main story because it deals double damage against foes that aren't holding an item. That's everything on this side of town, so enter the monorail to have a quick conversation with Professor Sycamore and Diantha. He gives you HM 02 Fly, which allows you to travel anywhere you've already been. Unfortunately, you can't use it outside of battle until you get the next badge. Ride the monorail to the other side of town once they leave.
The station on the south side of town has a man that gives away a Metronome. It increases the power of an attack that is used consecutively. The Pokemon Center is on this side of town. Mr. Bonding is waiting inside to give you the Befriending Power. This Poke Mart sells Timer Balls and Quick Balls, which are both very effective.
There's a girl inside the house south of the Pokemon Center that has a quiz. She mimics one of your Pokemon's cries and gives a Poke Toy if you guess right. It can be used to automatically flee from a wild Pokemon battle. The cliff to the north overlooking the other side of the city has a Sky Plate to pick up. The last thing in town is the gym. As promised, your rival is ready to battle, so heal up if you need to.
Now get ready to take on the Grass-type gym.