There is a free parking garage across from the entrance and a row of parking spaces behind the building on Central ave.
Walk Charleston. If walking is difficult, use a pedi cab or the free bus.
There's a parking lot near the shore a block or two away from oyster house. It does charge but it is not unreasonable.
I suggest walking, and leaving your car at your hotel. In this area you don't want your car towed.
We just walked from our hotel. We did use UBER around town some though. All good experiences.
Uber and forget about parking. Parking is free on Sundays though
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