As a relatively new SC resident, I am also still exploring but here are some ideas. The most important to us is always food. For lunch, try Surmet (sp?) on King St. It's good and is not too pricey. It's a little place located on a corner, just north of Charleston Place. For dinner, we like Hank's or the restaurants on John St. They vary in price points but are very good. Have Shrimp and Grits at least once!
You should definitely plan on spending a half day just walking around the area between Broad Street and the Battery. That's the older area and has the typical Charleston sideyard houses, beautiful gardens, etc. Also, a tour of homes or carriage ride can be fun.
Finally, if you like shopping make sure and set aside time for King St. and the Charleston Place shops as that is what they are known for.