Of Course, if you are a gun person, the Palmetto State Armory Stores in Summerville on the way in or out, and/or the PSA store in Mt Pleasant are worth a visit. Other advice given above is spot on. I would add that after doing the carriage tour, walk around on lower East Bay St, do the old market area, Cut through the Omni Hotel to King St and walk the King St shops up to about Marion Square, or maybe about 3 blocks more, and back down to Broad St. Also, go east of East Bay St out to the park along the Cooper River and walk down to the battery at the south end of East bay St. The Carriage ride on the street may be below the top of the battery, and the best views of the harbor and Ft. Sumter are from up on the Battery itself.
So, I would recommend getting all day parking downtown and call ahead to reserve going on the carriage tour first, for the history and layout of the area, then hit the "bricks" with a good guide map. Plenty of good places to eat downtown, some fancy and expensive and some not. If you like Greek Food, there is a place called Old Town at the corner of King and Market St worth trying. Its been there seems like forever.
Hyman's Seafood next to the Omni on Meeting St. has a checkered reputation. Some people seem to love it, but a lot of local's consider it a tourist trap. If you want a rustic dining experience with good seafood, use your Google Fu and GPS to find "The Wreck" on a back street (Haddrell St) in Mt Pleasant. Its on Shem Creek but its way back up in a residential area nearer to the mouth of Shem Creek, and its in an old fish processing plant. There are real Shrimp boat docks out behind it and some boats may be tied up there. Access to the boats and working dock is restricted, but you will be very close to them. Its at the end of the street, almost hidden behind a huge outdoor boat storage rack