From South Rim, go east to Highway 89 and then north to the Page area. Kind of dull drive until you get up to around Bitter Springs then gets to some grand vistas off to the west and north. Views of distant plateaus, Vermillion Cliffs, Colorado River canyon as it works it's way to the Grand Canyon. In the Page area is Horseshoe Bend and several slot canyons. Most well known are Upper and Lower Antelope Canyon. also Glenn Canyon Dam, bridges over the river, Lake Powell. A short drive on 89A where it splits off 89 south of Page takes you to the Navajo Bridges and Marble Canyon and the east end of the Vermillion Cliffs. Should you be staying in the Flagstaff area or just returning from Page or even looping from williams to South Rim, east to 89 and south again, the area between Flagstaff and the intersection with 64 has Wupatki and Sunset Crater Volcano National Monuments.
Easily reached between Phoenix and the Grand Canyon, south of Flagstaff is the red rock country of Sedona and Oak Creek Canyon. Take 260 off I17 at Camp Verde to 89A then north that way to Flagstaff. Montezuma Castle is a nearby cliff dwelling National Monument. Depending on time and interest, Jerome is nearby, an old mining town. Check out the various other national and state parks and monuments in the area around Flagstaff.