Rice, potato and corn are all great gluten-free carbohydrates. Cassava (Tapioca), Yucca and plantains
All rice is gluten-free, including glutinous rice (in this context, glutinous means sticky). Brown, red, jasmine, basmati, long grain, short grain, wild rice, forbidden rice, all gluten-free.
All potatoes are gluten-free, including sweet potatoes, Idaho potatoes and fingerling. In general, a foil wrapped baked potato is an excellent choice in a restaurant.
Beware of french fries as often additional ingredients are added to them or they are fried with wheat containing items.
Whole corn is gluten-free as is many products that are made with it. Be sure to check ingredients and cross contamination for items such as corn tortillas, cornstarch, corn flour, popcorn, etc.