I live in Columbia. Personally, I don't really like it. Well, compared to Clemson, anyway. I just like this part of the state a lot better. I don't actually live in the city limits of Columbia (I actually live about 5 minutes from Old Two Notch (saw that someone mentioned that) out near Pontiac).
You mention movies and places to see them. I usually go to The Movies at Polo Road since it's so close to my house. Wynnsong is the only other I've been to, I think, out on Forest Drive. As far as malls, you've got a pretty good selection. The main ones are Columbiana Place (there's a LOT to do in this part of town), Columbia Place (formerly Columbia Mall - they just renamed it and of course made it sound simliar to Columbiana
), Dutch Square, and Richland Fashion Mall. I've never been to Dutch Square, but the others are just fine.
I don't like the temperature and humidity in Columbia. I've heard it called the armpit of the state before and I definitely agree with it. It's downright unpleasant in the summer. Once it's not as humid outside, it's just fine.
As for internet, I don't think DSL was available in my neighborhood (Spring Valley) when we moved in, so we got Roadrunner from Time Warner. We recently switched to Earthlink, also done by Time Warner. Speeds are good enough for me. The only thing I have to judge it on at the moment (seeing as how I don't live there but 4 months out of the year and I'm not there now) is pings in Counter-Strike. I could usually ping 25-45 depending on server, so it's plenty fine for gaming. There's no monthly cap as for how much you can download that I'm aware, if that's a concern.
Traffic all depends on where you live. Two Notch Rd. has a pretty good amount of traffic on it no matter where you are (once you get close enough to Pontiac, it's not bad at all - on the way to Lugoff and Elgin). Traffic is never absolutely horrendous downtown from what I've seen. The city does have more than its fair share of awful awful drivers, though. People run stoplights constantly, among other things.
All in all, it's not a bad place to live, I guess. If I had the choice, I wouldn't live there (and probably won't once I graduate and attempt to find a job). It's just too hot and humid for me. If you do end up moving to Columbia, though, I'd agree with the statement that someone made about living in Lugoff, Elgin, Blythewood, Cayce, etc. Close enough to make the short drive into town to do things but far enough away to not have to hassle with traffic, noise, etc.