You're not very specific about destination, duration, type of shooting, or why you want to avoid the Grand Canyon. So here's a list in no particular order or location:
Antelope Canyons, Canyon X, Horseshoe Bend, Canyon de Chelly, Saguaro National Monument [east and west], Monument Valley [yeah, the scenic parts are largely in Arizona], Organ Pipe Cactus National Monument, Mission San Xavier del Bac, Chiricahua National Monument, Arizona Sonora Desert Museum, Old Town Tucson, Marble Canyon, Desert Arboretum Hiway 60, Superstition Mountains, and on and on.