I'm not a historian so this might get deleted, but I'm from the area. Boone Hall Plantation has a wonderfully preserved Plantation house and property complete with slave quarters and tour guides that will go into as much detail as you want about daily life at the time. Also you can get a tour guide for downtown Charleston itself. The Market area is kind of a tourist trap but there's still loads of history around those few city blocks. The "market" area itself is actually where slaves were taken off the ships and sold. Charleston is a beautiful city with tons of history, no doubt you'll have a good time.

I was thrilled with the Old Slave Mart Museum, however it is a lot of reading and doesn't have that visual impact. The Magnolia Plantation has an interactive tour through a few slave cabins which is quite an experience.

The Aiken-Rhett Museum has preserved the slave quarters which was an amazing place to visit. I seem to recall that you receive a recorded tour and are able to freely explore which I think would be ideal if you'd like to focus on slavery a little more than the main grounds. For example, at the Magnolia Plantation, you are only allowed 45 minutes or so to explore the slave quarters.

A formal guided tour that does hit all the "hot spots" regarding African culture as well as pre/post slavery is the Gullah Tour. The guide was great - passionate, knowledgeable and absolutely hilarious. You'll visit the market, the whipping house site, the Underground Railroad and many others.