There aren't too many places in Jacksonville itself. There is a small health store in the New River Shopping Center that offers a few gluten-free items. Food Lion on Piney Green Rd offers a good selection, Walmart also now offers gluten free items. If you are willing to travel Harris Teeters, Loveys and Tidal Creek in Wilmington offer gluten-free items.
As for restaurants, the best in town I have found so far is Outback Steakhouse, they have a dedicated gluten-free menu. Also Olive Gardens now offers a gluten-free pasta meal. Longhorn steakhouse also claims to offer gluten-free dining but I have not tried them yet. Just be sure to remind them that you do not want bread. Sometimes the waitresses that pack the food in take out bags forget and include the bread.