I will be stuck at The Renaissance STL Airport Hotel for the majority of week 48 (6th-11th Dec) due to a conference. This will be my first time St. Louis (let alone Missouri) and I'm completely unfamiliar with the layout of the airport area and the connecitons to the city.

Is there anything to experience in the surroundings of the airport/hotel after 4pm? How long and costly is the cab ride into the nightlife areas of St. Louis? I figured I'd hit up a martini in the evenings, chat up a few classy ladies, find a casino or some fine dining restaurants.