J - As a woman you can initiate, get the ball rolling, and then let the man do the work from there without pursuing. On Match for example you can initiate with a simple "like" of a man's profile and then let him take the ball and run with it.
I do agree though that being too available and a man knowing he has a sure thing can be a turn off. That is what I experienced with the Dr. which made me question how much a really liked her.
Honestly I would never meet a woman out for coffee on our first date. That said I could also not be with someone who didn't drink either.