Afternoon or evening, Intermezzo Cafe is definitely one of the prime spots for a date. It is very much in a European style. They have excellent cakes, some of them imported straight from Italy. The selection of wine, beer and spirits is amazing. They are also open late. I think until 4am (at least on weekends).
When I was living in Atlanta, this was my favorite late-night hangout to chat away with friends at the bar. Now, I'm not talking about loud partying and dancing... There is nice music, with dim lights and a great atmosphere; it's a place just to chill out with a nice glass of wine.
Oh, and I just remembered, try the hummus, a great snack to share.