This website tells everything you need to know about lumoise city.
It is the main city of all Kalos
There are cafes, resturants, and shops. Some of them can only be accessible if you have enough style, you can get style by doing various things in Lumoise city.
Cabs to get anywhere in Lumoise city easily, but the minimum fee is $710.
Prof. Sycamore lab'a is located at the south Blv.
Looker missions are located in Lumoise city, can only be done after you beaten the game.
The museum has Pokemon art
The train station will take you to Kiloude city, only when you have a pass given to you by Prof. Sycamore after you have beaten the game.
More info at bulbpedpedia.
Hope I helped!