StoOgE said:1960 and Twilight Struggle are pretty meaty 2 player games though the theme can be dry for some people.
If you are looking for something more substantial you could always go with War of the Ring (LOTR theme) or other Wargames. I'm sure there are other people that can better weigh in on these games.
edit: You might want to look at Through the ages which is essentially Civilization board game or even the above mentioned Endeavor which is Civilization lite. It has an official 2 player variant posted to BGG.
Fab, thanks for that, Stooge. 1960 might be a bit of a hard sell, but will definitely look into Twilight Struggle, and either Through the ages or Endeavour. I'll see which she fancies giving a go

War of the Ring might be good fun too - if anyone has played it and has an opinion either way I'd been keen to hear.