I think men like to do the asking. They like to feel in control. A girl shouldn't really have to ask, and if they do, then I would think it might make you come across as either easy or desperate.
Coffee or lunch - yes, I see that would be a better option.
This is cliched, but try meeting people with similar interests - evening classes, film clubs, etc.
Also a cliche but true - you're more likely to meet someone when you're not looking. Men can sense desperation. One day you'll go out in your worst clothes and not feeling particularly attractive, and men will flock.
A case in point - you say "coffee", filthiestfis says "date". I'm sure he's lovely, but you see how you get differing expectations! He also has some good advice...
Good luck and stop looking!