Hey,
I know Mount Pleasant Soccer Club runs Adult leagues for those of us in Charleston. They run a couple of Mens groups, level appropriate, and a Co-Ed league. I don't know when the seasons run because i haven't had time to play with them yet, but if you go to
www.mpsoccer.com, they should give you more information about their adult leagues.
There's also an 'indoor' soccer place for 6v6 called CitySoccer which runs leagues and you can also reserve the field for your own games as well. It's done on fake turf and with the indoor rules.
There is also a City of Charleston adult league. Most of the teams have sponsors, some don't. I know the College of Charleston occasionally fields some teams for the league, but I haven't played with the women since fall of 2004 due to time constraints.
CofC also runs competitive club programs for soccer as well as their usual varsity, so there is a good amount of young adults in the city who will play competitively.
As for pick-up games, I don't know anything about any prospective 'set' games. I know that some people, including myself, will take a ball out to Marion Square (corner of King and Calhoun streets) and knock it around for fun, but that's as close as I can think.
You'd probably have to get in touch with other people to see about maybe setting up pick-up games or finding people who will do them. There are one or two fields downtown, but I've never seen anyone playing pick-up there. Usually it's all Ultimate players, and then there are fields in Mount Pleasant, James Island, West Ashley, and North Charleston that may have some games.
I'd say to check the other local club sites, but I think most if not all of the rest are considered Youth clubs only. Mount Pleasant is working with the Rec Dept, so they have the added benefit of those resources on top of their Youth programs.
As for running...I can't think of any real running options that are popular with the students here. I'm not even sure we have a track team (okay yeah, I'm a really sad CofC student...don't rub it in). I know friends who will go running up the Ravenel for fun now, but not of any young adult groups...unless you count the El Cid cadets whose only escape is to go running, but they're out of class now.
Like somebody said though, summers here are brutal when it comes to the heat and humidity together, so anything you find will probably be restricted to the evenings (soccer), or evenings or mornings (running). Doing extensive workouts in the midst of the day's heat is pretty much asking for a coronary. Even doing stuff at around 4.30 or 5 can be incredibly painful; I remember one day the local health advisory was to stay inside and not do any physical exertion outside...and we still were out doing running on the Town Hall track in Mt. P while we trained for Norway. At least 2 or 3 girls got pretty sick during it.
If there's anything else I can help with, feel free to ask and welcome to the area.