For Tower Arch (as recommended by Timgco), pick up a map of Arches when you enter the park. The main access road, toward the back of the park near Devil's Garden is a two-way, dirt road and a two-wheel drive vehicle can drive it. However, just before you get to the pulloff for Tower Arch, there is a 4x4 road to the left that will eventually return you to the main park road. Fun road, but be careful, there is a pretty sharp decline about 2/3 of the way down the road that can surprise you. Taking the 4x4 road shortens your walk to Tower Arch by about a mile.
You will also see Eye of the Whale Arch and Anniversary Arch off the 4x4 road.
Potash road to White Rim Trail, or better yet, Shafer Trail down to White Rim Trail. Potash is accessible from 279, while White Rim and Shafer are inside Canyonlands Park. Not hard, but very photographic.
Long Canyon Road from the area around Dead Horse Point, again, not hard but great place for some photos.