Though the drive typically takes 2.5 hours, you can easily extend it to a half day (or more) of wonderful sightseeing opportunities. There are the viewpoints on the East Rim Drive to start with. Then after you exit the park, you'll be on the Navajo Indian Reservation. Be sure to stop at the Little Colorado River Overlook. This, as the name suggests, is a really outstanding view of the Little Colorado River gorge, which is more jagged and slot-canyonish than the Grand Canyon.
At the junction of Highway 64 and Highway 89, try to stop at the Cameron Trading Post. This is a real old West commerce center dating back to 1915. It's since been renovated and expanded and does look decidedly
more "touristy" than "rustic," but it still has a very fine collection of Native crafts, and the specialty of their on-site restaurant, the Navajo taco, is awesome! There are also roadside kiosks where the Navajos (and some Hopis) sell their crafts dotting the highway up toward Page.
If you don't mind taking a slight detour, you might pull off the main Highway and visit Lees Ferry, which is the site of an old ferry crossing and the historic Lonely Dell Ranch. You can actually drive your car pretty close to the Colorado River's edge here. Marble Canyon is cool too, a lot of times you can see the California Condors sunning themselves underneath the twin bridges. Maybe save your meal for Cliff Dweller's Lodge - surprisingly sophisticated food for out in the middle of nowhere!
Enjoy :)