Where do you find legendary Pokemon in Pokemon Y?

Answer 1

After you collected all the sliver things you can get mew but first you have to beat him at chase battle and hide and seek

you can get heatran on rydons bumper thing when you get all the highscores

you need a password for groundon darkria celebi and jirachey

you can get the others by completing the highscores on all of the minigames

ps: pikachu can have balloons,snowboard and a surfboard

Answer 2

In Pokémon Y, you can find the Legendary Pokémon Yveltal at Team Flare's lab in Lumiose City (Xerneas if you had Pokémon X instead), Zygarde at the Terminus Cave, Mewtwo at the Unknown Dungeon near the Pokémon Village and one of the birds inside Sea Spirit's Den at Azure Bay after a few encounters in the wild.

You can get Moltres if you picked Froakie, Articuno if you had chosen Chespin or Zapdos if Fennekin is your starter.

All of them are only available post-game except for Yveltal.