Quick paced card games can be a lot of fun in a very short amount of time. A very quick and easy game might be War, which is a game where two players split the deck and then lay down cards one at a time in strict succession. The high card wins and the game repeats until one player is wiped out.
A more enjoyable form of War is Hearts, or Crazy Eights, where each player draws eight cards to start with and then plays them according to their own impulses. You can play a higher or lower card of the same suit, high card wins, or play the same card in a different suit and force the change over in suits, or play an eight which is a wild card to change the suit to anything you want. A player who can’t play has to draw and keep drawing until they can. First one out wins.