I used to be a constant regular at Dad's, loved their improve and Scandal! as well as most of their plays. I have never been to Whole World, but I wholly endorse Dad's Garage, better location and a fun but hip vibe. Comedy hubby (who has performed at Dad's) characterizes Whole World as a little more stagey/rehearsed/"sitcom-y."
Hit up Fritti or Barcelona beforehand, that sounds like a nice date.