The best place to dock to be able to access downtown is the Charleston Maritime Center. It is only a five minute walk to the Harris Teeter grocery store, Starbucks, numerous restaurants and pubs, and excellent tours of the homes and sights of Charleston. As you enter the harbor. the lower range marker is located on their fuel dock.[right across the Cooper River from the aircraftcarrier "Yorktown"]. It is an awesome sight to view the docking and unloading of MSC containerships, as they dock just a couple hundred yards to the north.
Just keep in mind that the Maritime Center facilities have NO protection from the currents, so docking there at times other than near slack can be interesting at best. They are, pretty much, the only facility that is right downtown that you can tie up at.
I have often stopped at the City Marina, on the Ashley River (Charleston City Marina - Home of The MegaDock) It's about a 10-minute walk to downtown and they also offer a free shuttle service to most downtown destinations, will return to pick you up, along with your groceries or whatever. Similar free service to West Marine. It's about the best-run marina that I've encountered along the ICW. There is also a good anchorage directly across from the marina. Last time I anchored, a $5 dinghy fee at the marina would buy you most of their ammenities. Much of what you'll need are right onsite - restaurant, sail loft, some groceries and other supplies, booze, etc.