Begin with a carriage tour from the City Market area. Then walk. Visit the Nathaniel Russell house on Meeting St and purchase tickets for the Aiken-Rhett house at the same time for a discount. One, the Russell house, has been restored to its glory. The other, sits with original wallpaper peeling, carriages still in carriage house, etc. Fascinating! Take one day to visit one of the these plantations: Drayton, Magnolia, or Middleton. Visit the Angel Oak on John's Island, it's free and amazing! Folly Beach, Sullivan's Island, or Isle of Palms for beaches.
Good restaurants near the Church St Inn are Sweetwater (breakfast), Hanks Seafood, Fleet Landing, Carmella's Bakery, Slightly North of Broad, Magnolia, Blossom, Tradd's, Pearlz, Minero (Mexican), Brown Dog Deli ....I could go on and on but those are walkable.