A detailed answer please for the benefit of others!
let's start
Name Effect Combination Colorful Shake Increases happiness Any two different colored berries Rare Soda Increases level by 1 to 4 1 Lansat Berry + 1 Starf Berry Ultra Rare Soda Increases level by 4 to 5 N/A Purple Juice Increases HP EV by 4 to 32 Two purple berries Red Juice Increases Attack EV by 4 to 32 Two red berries Yellow Juice Increases Defense EV by 4 to 32 Two yellow berries Blue Juice Increases Special Attack EV by 4 to 32 Two blue berries Green Juice Increases Special Defense EV by 4 to 32 Two green berries Pink Juice Increases Speed EV by 4 to 32 Two pink berries Perilous Soup Resets EVs to 0 1 Kee Berry + 1 Maranga Berry
Restaurant le nah on south boulevard. 3,000 pokedollars, they only serve double battles. the prize is 15 tiny mushrooms. here are the trainers to battle:
first battle: Chef roger with pansage (lvl 10 male) and pansear (lvl 10 male)
third battle: Chef roger with pansage (lvl 10 male) with panpour (lvl 10 male)
restaurant le yeah on autumnal avenue. 15,000 pokedollars. they serve triple battles and rotation battles. the prize is 20 big mushrooms. here are the trainers:
first battle: Waitress Talia with mantine (lvl 31 female with king's rock), emolga (lvl 31 female with king's rock), Sigilyph (lvl 31 female with king's rock)
fourth battle: Chef Albern with simisage (lvl 31 male with liechi berry), simisear (lvl 31 male with petaya berry), simipour (lvl 31 male with salac berry)
Restaurant le wow on hibernal avenue. 100,000 pokedollars. double battles, triple battles, and rotation battles. you need to be the champion. the prize is 25 balm mushrooms. here are the trainers:
first battle: Owner Christophe with qwilfish (lvl 63 male), druddigon (lvl 63 male), ferrothorn (lvl 63 male)
fifth battle: Waitress Paula with chatot (lvl 63 female), exploud (lvl 63 female), aurorus (lvl 63 male)
sushi high roller near rouge plaza. you need to have started the Looker missions to get in. 500,000 pokedollars. double battles, triple battles, and rotation battles. the prize is 25 big nuggets. here are the trainers:
first battle: Furisode Girl Gwyneth with cherrim (lvl 65 female), ninetales (lvl 65 female), tropius (lvl 65 female)
Services
Transportation
Facilities
Shopping
Fine Dining
Cafés
that is what you can do!
http://bulbapedia.bulbagarden.net/wiki/Lumiose_City This website tells everything you need to know about lumoise city.
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!