There are lots of places to play, but it really depends where you are. You can check out this list at the CT State Chess Association Website (http://www.ctchess.com/index.php?sect=play), but I don't know how up-to-date it is.
I play once or twice a week in the Norwalk area (see http://www.geocities.com/norwalknights/meetings.htm). I'd also be remiss here if I didn't mention that this club is holding a tournament on June 7th (see http://www.chess.com/event/view/norwalk-chess-is-back2), which will be USCF rated but a much more casual affair than other tournaments in the area.
There are a couple of other southwestern CT meetings that I know of...I think some players meet on Monday evenings at one of the Burger Kings in Bridgeport...I can find out which one. My sense is that there is a lot going on in the UConn area (at least, there are a lot of smaller tournaments listed in Chess Life magazine) and around Yale in New Haven. And in early August there is a big tournament up in Windsor Locks (http://www.chesstour.com/brad08.htm).
Failing all that, you might want to try http://chess.meetup.com/. It never seems like there's a whole lot going on with those lists, but perhaps you can start your own group.
Drop me a line if you're interested in one of the Norwalk meetings.
any one out there in Connecticut know where I can play chess face to face?