I haven't been yet, but DH and I are doing a mini trip to Charleston in April (high season). Everyone on the Charleston TripAdvisor forum says the historic district is the place to be, but FYI hotel rooms are pricey. We are staying at the Barksdale House that is in the Historic District, and paying a base rate of about $260 a night for a king room (but that's before taxes). If you go with a queen room, it's a little less. It's a little guest house that gets good reviews, looked nice to me, and was one of the less expensive places that was close in, in the historic area. I was originally looking to stay at somewhere more at the $200 - $250 price point including taxes and fees, but I wanted a good location for walking to stuff and ended up upping my budget to $300 a night to get that. I'm paying with taxes $890 for a three night stay.
I know many people on the TripAdvisor Charleston forum that don't want to spend that much on a hotel room stay in Mount Pleasant and drive into the historical district for the day or a few days. Rooms are way less expensive there, but you are giving up the walking to historical attractions right from your hotel part.
Note that the time of year you go affects hotel rates too with nice weather times (times where it's not too hot and not too cold) typically having the highest rates.