Bull Street Gourmet & Market & Persimmon Cafe are two of my favorite low key, super delicious lunch spots in Charleston. 

For a fun evening out, I would visit Theatre 99 they have wonderful improv shows that are actually funny! Local and visiting stand-ups visit often as well. It's a small theater located above a bike shop, full of charm and wonderful performers.

Broad question as there is so much to do.  On Upper King Street there are loads of great places to eat - The Rarebit, The Macintosh, The Ordinary, Prohibition just to name a few.  On Queen Street in 100 yards there is a Napa Vally winery tasting room and 3 of the best restaurants in Charleston (Poogan's Porch, Husk and 82 Queen St - Great bar at Husk too)

Couple of neat roof top bars - 225 Market St, Vendue Inn and a new place on Meeting Street in the Grand Bohemian.

Hidden gems - Leon's, The Gin Joint, Crave in Mount Pleasant and Rita's Seaside Grille at Folly.