Good Bar (Stuttgart)

Hello all, I need some advise. I am so new to the area and have not yet had a chance to get to know the downtown bar scene. I potentially have a date with a new friend and would like to meet downtown for a drink. I am on the S1 line and am looking for a place that is classy, but I won't be embarrassed to walk in by myself and sit at the bar. Somewhere I can walk over from the Stadtmitte station. Suggestions please! I am in uncharted water.