Old City Market - Located on Market Street in the downtown, its an open air market (covered from the sun) where local vendors sell their stuff. You can find anything from touristy t-shirts to jewelry to sweetgrass baskets. Its surrounded by restaurants on Market Street, so if you get hungry you can pop your head in any of the places for a bite to eat.
Battery Park - A huge park right on the coast is a must see. The park itself is beautiful!
Rainbow Row - One of the coolest parts about Battery Park is that you can walk along the ocean for two sides of it, and on the other sides, you can see the huge mansions of "rainbow row".
There is a carriage ride that you can take as a tour around the historical downtown. The tour guides tell you all about the buildings, who lives/lived there, the history, etc. I have never taken the tour, but I've heard its fun, and I did take this picture of some unsuspecting tourists.
King Street - King Street is home to tons (and I mean tons) of shopping. You can find everything from tiny boutiques and antique stores, to Gap, or Starbucks, right next to each other. I normally do more window shopping than buying, but it is so fun to wander the streets.
Waterfront Park - This is another park on the coast that you get to via cobblestone streets. There is a great view, lots of benches, and a fun fountain.
Folly Beach - Its about 15 minutes from downtown (south), but its gorgeous! There are a ton of beachy restaurants to grab lunch or dinner and the beach houses are so fun to look at!
Sullivan's Island - Its also 15 minutes from downtown (northeast), and a little quieter than Folly Beach, but still gorgeous and very relaxing. It is a laid back, family friendly place.
Isle of the Palms - 12 miles from downtown, just past Sullivan's Island and very similar. They even have a park on the beach.
Basil - A Thai restaurant right on Kings Street. Its delicious! I would go back in a heartbeat.
Poe's Tavern - A beachy place on Sullivan's Island with unique American food. Try the fish tacos! yum.
Other than that, I'm sure any restaurant you try will be good. Charleston is known for their Shrimp 'n Grits, so make sure you try them while you're there.
If you stay at a hotel in the city, you can take a rickshaw to get around. They work solely on tips, and it is very fun to ride in the open air and get a mini-tour on your way to dinner.
Other things to do:
Ferry ride to Fort Sumter
I'm sure there is a whole lot more, I am by no means an expert. I love the history of the city and how beautiful it is. Emily, let me know where you decide to go!
Anyone have any other ideas for things to do in Charleston? Or other fun cities in the US that they might want to visit for their anniversary trip?