Men who are strong, confident and independent.
As for mystery, a man who she needs to work for to break down the outside walls. Causing her to feel unique and special in the man's life.
People in general want what they can't have...
They want to screw with our minds.
Confident and funny....most basic way of describe their wants...
moreso a guy who can fulfil their primal urges and needs as a male should.
Basically they want a man who acts like I man,thats why sweet guys get nowhere because they want a relationship and try to provide a fairytale when girls want something thats actually real and serious if they want a relationship too.
But its basically just like this
For one night stands: A guy who their attracted too and would want to have sex with simple, they don't have to like you at all, but if they would let you have sex with them then you got yourself a One Night Stand
For Day 2s: connections on a deeper leve like common interests or reasons she'd be interested in dating you
For real relationships or something deeper: being able to fulfil her personal needs as a woman and acting like the man you should be.