I realize this post comes late for the original poster but hopefully will be helpful for others with children. I'd give a whole 'nother list to someone without kids. All of the upscale restaurants are real good at adapting meals for gluten free eating. (My favorites include La Fourchette, the Charleston Grill, Cypress, Tristans and Blossoms.)
Moe's is a chain mexican restaurant on King St. near Marion Square, very kid friendly with free kids night on Tuesdays I think.
Santi's is a mexican restaurant on East Bay/Morrison Dr. about a mile north of the Ravanel bridge.
In Mt. Pleasant there's a Moe's across from the Whole Foods on Houston Northcut. There's another tex/mex restaurant that's kid friendly called Uno Mas on highway 17 N that is really good. It's owned by the people who run the Mustard Seed restaurants in Mt Pleasant and James Island which are great for a more upscale but still casual family meal.
Sticky Fingers BBQ restaurant on Meeting St downtown is very kid friendly and most of their sauces are gluten free, but for BBQ it's best to head to West Ashley and go to Home Team BBQ on Hwy 61.
The Boathouse seafood restaurant on East Bay downtown is another good option for an upscale meal with kids as is Rue De Jean (french bistro fare) on John St. downtown.
Places I'd avoid for gluten free dining include Hyman's seafood, Jestine's, Hominy Grill, and the Wreck as they have a lot of fried foods and there's a limited selection, although Hyman's will grill or broil your meal I believe. The first three are major tourist traps as well.