In the board game theme, have you tried any 2-player abstract strategy games? Some of my favourites include:
Quarto (complex 4-in-a-row game with a twist: your opponent chooses the piece you must play)
Quixo (from the same publisher, Gigamic - tic tac toe on steroids with an ever-changing board)
Hive (each piece moves a certain way, very portable defend-the-queen game)
Tak (simple rules, deep strategy - connect opposite edges of the board while preventing your opponent from doing it)
Not strategy, but abstract speed game: Nine Tiles by Japanese company Oink Games (not Nine Tiles Panic, tho that one isn’t bad). Oink has very clever, easily packable party games and a few can be played with two people.