Fascinating museum. Parking is awful but if you're lucky and patient you will find a space within five-six blocks and the walk is beautiful...even better is the Kingsley Plantation in Jacksonville Fl. It's free unlike most of the restored plantations in the area. Have been a half-dozen times and am still shook up. A must see if you are traveling south into Florida...
From the visitors center you can take a free bus to parts of the city. "The best place to park is the Visitor Center at 375 Meeting Street as a central location with many public transportation options. The parking garage offers easy access to the Visitor Center to start your day in Charleston – with restrooms, a gift shop and information center to get advice and maps to walk around the city. The Visitor Center Parking Garage is also one of few places that has spots for RVs and electric plug ins."
Parking isn't great in that area. We left our RV at the campsite and drove down in the truck.
No rv parking down there that I saw but you've got other options from others who answered before.
There are lots of parking area around the market site
I think you will have to park in one of the many lots around the city
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