The Hatch Point campground is about 25 miles from US 191, first on good paved road (the Needles Overlook road) and then well-graded gravel road (the Anticline Overlook road). It's a small campground, nine sites with pit toilets and water, and it was very quiet when I was there; only 2 other sites occupied, one by a couple from Durango with a Scamp trailer of their own. Site #1 has great views.
I drove out to the Anticline Overlook and Minor Overlook, and oohed and aahed over the views there.
The BLM information sign mentioned a hiking trail, so I figured I'd better check that out. The Trough Springs trail is a down-and-back-up trail, 2.5 miles each way. The total descent is 1100' but the majority of that comes in the last mile as the trail descends a steep rockfall section of the canyon.
At the end of the descent is Trough Springs, a pretty oasis. From Trough Springs it is a mile or so down to the Kane Springs 4WD road (accessible from Moab). The Trough Springs trail was well-cairned but it didn't appear to get much use at all. I didn't see any recent tire tracks at the trailhead, or any recent footprints on trail except for one set of tracks down at the very bottom by the springs. It had been rainy the previous two days, so that had reset the track-meter as it were.
Trough Springs GPS log and pictures at EveryTrail.com
The next morning I rode the mountain bike out to the Canyonlands Overlook, about a 13-mile roundtrip from the Anticline road. The Canyonlands Overlook road is signed as "4WD Required", which I would agree with. The first 5.5 miles are mostly easy 4WD high clearance; there is one stretch of sand about 4 miles in, maybe 100 yards long, that might be a little bit tricky. At about 5.5 miles in, there is a small turnaround area with a nice overlook to the north. Beyond that point is technical 4WD, not suitable for normal road vehicles, but very nice intermediate mountain biking. It is about 1 mile to the Canyonlands Overlook itself; pit toilet, picnic table, and more killer views...