When it comes to deciding on a great 2 player game, you can never go wrong with playing a round of 7 Wonders Duel.
What I find great about this game is that there are three distinct ways to win the game. Two of these ways end the game early: Military Supremacy and Science Supremacy. If you manage to keep your opponent at bay in these two areas (and you yourself don't win from them), you can still win by having the most points at the end of the game.
Once you have an understanding of the rules, 7 Wonders: Duel is a quick and fun game to play. How to play: