Boone Hall Plantation. Middleton Plantation. Going to see the Angel Oak on Johns Island.
Taking a walk in the Market is a tourist must ( though IMO they sell mostly junk ) and walking Rainbow Row. I personally would recommend the ghost walk. It's a lot of fun and even non tourists enjoy it. But, watch the sidewalks, we see lots of trip and fall injuries from uneven cobblestone.
When you're downtown, you can have dinner at Tommy Condon's on Church St. Except for Monday and Tues they have an Irish band, who are really good ( and also friends of mine

) I think they have a prime rib special one night...There's lots of shopping on King St and a nice outdoor mall in Mount Pleasant ( The Town Centre- it also has a 16 screen theatre )
If you need anything else, let me know.