Well, I'm a woman, but since I'm lesbian, I think I'm qualified to answer this question.
Well, although just good looks can get my attention, what I really like in a woman is intelligence. So I guess I'd think "I wonder if she's smart too"
No matter how good-looking or cute, if she is dumb or not interested in science and thinking, I stop being interested.
And I'd probably wish I'd had the courage to go talk to strange people. But as I don't, I'd probably just try to stare at her in a way that doesn't make me look like a creepy stalker.