However, there is only one place to do them, Lilycove City. This is where you'll get your Contest Pass & Your Pokéblock Case. You can also Blend Berries Here.
You can do all types of Contests here; Normal Rank, Super Rank, Hyper Rank & Master Rank for all of the types; Beauty, Tough, Smart, Cute & Cool
Contests are the same format as in Ruby & Sapphire so it should be second nature to you by now: