I usually just plan to be stood up and go see a movie or browse in a bookstore afterward. This works for me more than half the time. However, I don’t recommend it.
Seriously, a first date should be relatively short and fun, offering a way to escape if it doesn’t work out, or alternatively, a way to extend it if things are really going well although the PUA gurus all pretty much universally recommend cutting a first date short to MAINTAIN her INTEREST LEVEL and STIMULATE her CURIOSITY about your MYSTERY. (I get a headache just reading this shit, but I have to admit that these guys get laid more than I do.)
I don’t think the activity matters terribly much, as long as it gives you something to do or talk about that isn’t so engrossing that you can’t focus on each other. Going to a coffeehouse or mall and peoplewatching offers both a way to keep things light and interesting and at the same time evaluate her style of interaction and humor to see if you mesh. I like used bookstores, but that’s not to everyone’s taste. Museums and arboretums and the like are a little dangerous, as it really forces you to stay there for a certain minimum of time even if it isn’t working out, and often makes for awkward, stilted conversation. Ditto for bowling or something like that. Basically, keep it loose and open, and if possible, something that is of mutual interest.
Try watching Before Sunrise to get some ideas; it portrays “first date” type situations more realistically than any other movie I’ve ever seen.