Cool girl you have to want to play sonic and adventure games.
Gabrial Knight doesn't focus on shooting, I'm not sure about the newest Alone in the Dark.
The Longest Journey is a new ones that's nice.
Also, you'll want ot play leisure suit larry with her, the last one was Love for Sail, very funny and sexual, if your relationship is at that point.
I only have a bit of experience in adventure games, try doing some googling and look for top10's, etc. You can find big reviews that'll help you out.