The Upper East Canyon is home to seemingly countless little cracks and canyons, many with no official names. Shelf Canyon is one of the more interesting little canyons worthy of exploration. Although it barely shows up on a topo map, Shelf Canyon is the first prominent little canyon east of the Canyon Overlook Trail (on the north side of Route 9). Park in one of the little Canyon Overlook overflow parking lots for easy access. Note: I credit Ram for naming this canyon; many people know it by this name and it definitely suits the geology of final section of this hike.
The hike up Shelf Canyon is a fairly short one: 1-2 hours to go less than half-a-mile up this little drainage. From the road, find the easy little route into the wash, then begin hiking upstream. The first section of the canyon is fairly uninteresting -- wide-open and overgrown with trees and bushes. There are also a few boulders and sections of slickrock that require careful scrambling to get over. (If you are not used to scrambling on slickrock, they may be a bit intimidating, but they are not too difficult.)
In less than a quarter mile, the walls narrow up and you are in a beautifully tall and dark little slot canyon. With less vegetation, the going actually gets easier, but there might be a small pool of water that you need to wade through. The canyon ends in a nice little alcove with many cool ledges (shelf formations) going up the west wall. It's fun to do a little rock scrambling here to work your way up the ledges, but be careful as it can be more difficult/dangerous to get back down. Once you have gotten your fill, return the way you came.
This hike probably won't excite everybody, but it would be a fun one if you're looking to get off the beaten path. The few little rock-scrambling obstacles seem to keep the general public out; I wouldn't recommend this for those with small children. The final alcove is definitely a cool spot, but my only complaint is that as soon as the canyon gets interesting, the hike is over!