just keep in mind when you're playing that you're not doing it to impress her... you're doing it because you feel like having a jam session.
i think thats probably the best mindset to have in most aspects of PU. you're doing it because you want to, not to impress her.
i'll often just leave the bedroom (especially good for freezeouts) and go play in the livingroom, because i want to play (not many things gets attention like a cool riff

).
i keep my acoustic in the bedroom, so if we're watching tv or whatever in the livingroom i'll get up, play in the bedroom and she'll come watch (and get wet(ter)

)
as for what to play... yes, it would depend on the girl... but it also depends on you. i normally play whatever i feel like though. it's been established that i'm a metalhead so i'm going to stay congruent with that... it'll look weird if a guy wearing a "as i lay dying" shirt starts playing some pop-culture song.
if she's nice i might throw in a little "tears in heaven" or "stairway to heaven"