I live in a large urban area and suspect there are groups of independent game developers that meet to discuss games and just hang out. Are there any clubs or groups or associations or whatever for indie devs?
Yes! Indie developers tend to be very social. Without knowing which city you live in, it's tough to say what's available, but check out the IGDA's chapter list:
Though these events include students and non-indie industry members, your fellow indies will often be there in force. For example, here in Boston, we have the Boston Postmortem group which meets monthly:
And there's a large enough dev scene in the Cambridge/Boston area such that we even have a monthly meeting specifically for indies:
Generally speaking, once you start networking with other local indies, you'll find out about everything that's going on in your city, whether you want to or not.
TIGSource has a forum for get-togethers at http://forums.tigsource.com/index.php?board=15.0
If you're in NYC: http://www.nycgameindustry.com/
Portland, Oregon, USA: http://pagdig.org has a monthly get together
For anyone in Seattle please join us at the Seattle Games Co-op. We currently meet twice a month, once to present a topic of interest -- say Blender or Linear Algebra -- and once just to hang out and have a beer.
We're always looking for fellow game developers to participate and we're planning a lot of great stuff for the future, so get involved now!
For the Cambridge, UK indie scene, including Chris Delay of Introversion and the creator of VVVVVV, see Cambridge Friendship Club.
In San Francisco I would recommend the http://www.meetup.com/SFGameMonetization/
They run workshops and regular drink meets. There is a good mix of indie and established developers that attend.