We visited a couple years ago in October - it was still awefully hot and humid. We walked 9 miles our first day! Then we found out there were buses you could hop on and off!
1. Drayton Hall (plantation) is a must. All original and preserved - not restored so mainly for the architechural detailing. The mansion is empty, but you get to see all the building details. There is also a nice museum on sight with furniture etc. I would plan to spend half a day at least with the house, museum and grounds. Yeah, the grounds are amazing - look out for alligators!
2. Heyward-Washington house. Has the famous hutch. Unfortunately you can't get close as you can only look in the room. This place was the highpoint for furniture.
3. Joseph Manigault House. As I recall this was a little later period (early 19th century).
4. Aiken-Rhett House. A little later still in the 19th century. I think this was the last house we visited before moving on, and was the least impressive - but still well worth a visit. More 19th century decorations.
5. We visited another plantation (Middleton Place) as we were leaving. The main building is gone (foundation ruins still exist), but one of the other buildings can be toured (like a smaller mansion). This had a famous table table attributed to Thomas Elfe. The tour was extremely dark, and you could barely see any details on the furniture - very disappointing. The guide did let me borrow his flashlight - which needed batteries

so I could get a better look, but it kind of sucked! The grounds were also amazing.
6. You could spend hours just walking around the old city. There is a group of colorful (yellow, pink...) mansions facing the ocean. We didn't get to spend much time visiting that area because a hurricane was coming in!
FYI, I miss the days when there was new content daily on the Forum.