I wouldn't necessarily recommend all these for two players - and some of them I wouldn't recommend full stop.
I'd agree with most of Shobu's suggestions and also add Squadro (another neat two player game from the same line of games as Quoridor and Quarto by Gigamic).
I also think Buttons works well as a two player game - one of those games that's a little tricky to explain but actually very simple to play.
Also, I'd probably want to draw your attention most to Lost Cities and Jaipur (in that order) from Shobu's list.
