Just over the river in Mt Pleasant are several hotels (Holiday Inn, Red Roof, Hampton Inn, etc). That's a lot cheaper than staying in the historic district; it's not as scenic and cool, but definitely cheaper (I've done both, including a B&B on the battery). I flew into the East Cooper Airport (KLRO) on our last trip. That's a nice little airport, but I think I may go into KCHS for a short weekend trip next time.
There are lots of things to do in Charleston. Patriot Point has old naval vessels. There are lots of golf courses. Shopping on Market Street is very interesting. We enjoyed a horse-buggy / history lesson ride last time. They have an aquarium, but it's a lot smaller than the Atlanta and Chattanooga aquariums.
Touring the houses in the historic district is nice. I prefer doing in on a mountain bike. That's faster than walking, but easier to stop and look longer than when you're in a car.
There's also sailing tours of the battery / harbor. I haven't been on a tour of Fort Sumter yet.
Don't go too far into summer. It can get quite hot in Charleston. And while the water may moderate the temperature it also cranks up the humidity.
The WTA Family Circle tennis tournament is in mid April.