To get you started these sites,
discoverourtown.com and
charlestonsfinest.com gives recommendations and more information on pretty well everything.
If time is limited there are 2 areas to head for, King Street for more upscale shops and the Old City Market in Market Street between Meeting and East Bay Streets.
Built in 1841, this historic market area is filled with vendors selling local art, books, baskets, books, clothing, souvenirs, and handmade sweetgrass baskets in its many small shops, restaurants, flea market, and seasonal farmers market.
This is where you can buy a souvenier sweetgrass basket and see them being made. Don't bother shopping around for a better price as the vendors seem to have got together and decided on standard charges.
If you are visiting by car a word about parking as you don't want to waste precious time driving around looking.
If your stay is short there are parking meter areas.
For longer stays here is a map showing garage parking sites ci.charleston.sc.us
As so many areas are for residential parking the garages are your best options.