The trek up to Hidden Valley, a valley between Moab and the canyon rim, begins abruptly switching back from the trailhead. The valley alone is beautiful and would be worth visiting, but the trip is made even better by the vast number of petroglyphs found at the valley's head. There are also two distinct rock circles, which are thought to be from ancient peoples.
In the spring, fall, or winter, Hidden Valley is a good hike (with no snow on the ground). Get an early start if you're doing it in the summer. The steep part receives morning and midday sun, and by midday, it would be extremely hot.