I'm in St. Louis as well. I host a meetup.com group for Axis and Allies. We play the board games, currently the newest ones: AA1940 versions.
Here is a link to our organization:http://www.meetup.com/St-Louis-Axis-and-Allies-boardgamers/
I host events at local game stores the Second Saturday
and Forth Sunday
of each month.
Other members sometimes host events as well, and when my wife is on afternoons I host events the other weekends of that month, in our finished basement.
We have about 10 active members out of 45 or so. We usually have 1 to 2 games running at each event. The game stores will accommodate 4-5 game tables if we grow large enough.
Skill levels range from new, to classic game, to veteran. We are friendly and eager to teach new players. You can just watch if you are so inclined as well.