I've always been against the "let's hang out" mentality, but I am older than you guys. I suppose you can get away with it as a late teenager or in your early twenties, but later on that phrase becomes a real negative.
A woman wants a man to take contol and command. I usually decide to do something first, and then tell her, "I'm going to such-and-such this saturday. Why don't you come on out with me". I just set up (via e-mail) a date with a woman by saying, "I see you and I spending a day at {insert amusement park here}, and then in the evening going over to the stadium to watch {insert band here}. If you're interested, let me know.
That was 3 weeks ago, and I'm still waiting for her reply. Just kidding! She immediately said she would love to go.
That conveys a take-charge., masculine presence. "Let's hang out sometime" is weak, weak, weak by comparison.