Whenever I have friends or family come to Charleston, I always recommend that they take a carriage tour of downtown, it is the best way (in my opinion) to take in as much of Charleston while relaxing and learning at the same time. Unfortunately, most tours stop running at 5pm during the summer, so that would be a logistical problem.
The next best option is to take a guided Haunted Tour. Mitchell mentioned it and it is something that is offered typically only later in the evening. They take you through several very old buildings (Revolutionary War period) and it can be entertaining, especially in groups. I've gone on one, and the only thing I would have done differently was to not do it on Halloween (drunk revelers kind of ruined the mood).
I don't recommend the Aquarium, it is too expensive for what it is and it closes at 5. Booking a harbor cruise would be fun, drinking/partying while cruising around on a boat that could handle the entire conference! They run all the time and feature regular club type parties or live jazz bands. After that, here in the Holy City the only thing we have more of than churches is bars, so there will always be a stool to pull up and it would just be a matter of finding one to host a party. Some of our Barcamp Charleston organizers would be a better source of information for that.
As far as pizza goes, Mellow Mushroom is at the top of my list, followed by D'Allessandros (small place) and Andolinis. Mellow Mushroom is on King St, a block and a half away from the conference, and is an average sized place and always busy. Andolinis isn't 'gourmet' pizza but they can handle around 50+ people at a time I believe, and it is less than a block away from the conference. I order carryout from them every week for my student ACM club meetings. D'Allesandro's is small and cheaper but a 'local' kind of pizza joint. All of them deliver/cater I believe.