We visit Charleston every year. There’s no place like it anywhere. It is easily our favorite city. One night isn’t nearly enough time, though. If it were me, I’d go there instead of Savannah. ;-) Anyway, you’ve gotten some great suggestions above. I don’t want to repeat what people have already said, but I wanted to add a few things.
First, make dinner reservations ASAP. Some of our favorites in the historic district include Husk, Magnolias, SNOB, Charleston Grill and Peninsula Grill. The Obstinate Daughter on Sullivan’s Island also is wonderful (you will need to drive there).
I saw someone refer to “downtown” above. There is a definite distinction between downtown and the historic district. Downtown can include/border some very sketchy areas. You want to stay/be in the HD.
For lodging, the French Quarter Inn is amazing. And a great location in the HD. Walkable to everything.
I don’t think anyone mentioned the Ft. Sumter tour. It’s a 30 minute ferry ride each way to get out there and back, and you’ll have an hour to explore when you’re there. Truly an amazing thing to see.
If you do decide to go to a plantation, we love Magnolia Plantation. The gardens are amazing. You also can take a swamp boat tour.
Make time to just walk around. Be sure to walk to the Battery to check out the park and also the amazing homes down there.
If I can answer any specific questions, let me know. Have a wonderful time!