Dana Plato's character from Night Trap. The date would begin with me creeping around behind her, trying to kill her with an electric drill. Then a panel would open up in a wall, I would stupidly walk into it, and that would be it for me.
All jokes aside, I'd go out with Hisui from Tsukihime at the drop of a hat. The psychological strength of that girl is remarkable, but she gets easily flustered by unexpected things (just like real people) and is utterly adorable at those times. I'd love a chance to put a smile on her face. I'd probably take her out for a picnic or something, anything to get her away from Tohno House.
That's a reference most people won't get, so my second choice would probably be Irene Lew, 80's hair and all. She was the iconic female of the NES era for me, more so than Peach, Zelda, or Samus Aran. Probably because Ninja Gaiden actually had a story that unfolded inside the game instead of inside the instruction booklet. I'd invite her out for a night of dinner and live theater, but she'd get called away during dinner for a CIA op in a rainforest somewhere and then I'd never see her again, probably.
Honorable mention goes to King from Art of Fighting. A tough, independent woman who owns her own business, is an incredible fighter, and feels no pressure to conform to society's norms regarding female beauty, but is beautiful nonetheless. I am at a loss as to what we'd do on a date, though. Bowling, maybe?
Instead of spending an hour and a half trying to come up with thoughtful, detailed answers, I should have rattled off "Lara Croft" like everyone else and gone to bed on time, but hey, them's the breaks.