Picking up the tab: as a personal rule I ALWAYS pick up the tab on dates. UNLESS it was the lady who asked me out and insisted on paying. Being an old-fashioned sort from the 20th century though I get a little wary about women asking me out unless they're one of those close friends / coworkers you've worked with for at least a year / relatives / former bosses / ex-future in-laws you are still on good terms with.
First date place? Don't try to get too cute or clever or try too hard I always say. First dates can get tense enough on their own without you having to worry about being cute / clever / trying too hard. Here's my rule of thumb: it has to be a place with waiters, and they have to let me in wearing shorts. If not then it gets too fussy for me. Also, try not to do a first date after office hours; you'll be a little dicky after a day at the office.