Where is your rivals after beating the elite four in Pokemon X?

Answer 1

Your competitive rival - Calem or Serena, depending on your chosen gender, can be found in Kiloude City after accepting at least one match in Battle Maison. You can battle him/her once each day- their team doesn't change with each rematch, but the experience and cash reward is very good.

Shauna, the weakest rival, can be found in Veneville Town. You'll receive a starter Pokémon from her, dependent on which of the three you chose at the beginning.

Tierno, the guy who prefers to study Pokémon's movements and often talks about dancing, can be found in Coumarine City. He'll ask each day to see a specific move.

Trevor, the shy guy, can be found in Geosenge Town post-game. He'll tell you about the Pokémon who can use Mega Evolution.