I did a backpack trip from Island in the Sky down a trial near Upheaval Dome to near the Green River. The bummer part of this is we hiked several miles along a trail to the zone we were allowed to camp, and we see an old Cadalac drive by. It turns out we were close to the northern part of the White Rim road and the spot was not so great.
Camping is also allowed near the junction of Upheaval Canyon/Syncline Valley, which is a long way from the road (and which almost always has good water). Other than there (designated campsites) and the White Rim Road (where you camped), camping isn't allowed on that hike. Almost all of the rest of the Island in the Sky area below the rim is open to free-range backcountry camping, without designated sites.
My favorite backpack in Island in the Sky is along the White Crack Trail (which isn't marked on the park maps, but is begins at the White Crack Campsite and is easy to follow until you are near the river), to the Colorado River via Stove Canyon and to the Confluence Overlook (each of the three regions in Canyonlands has their own confluence overlook).
The rock formations are spectacular as are the views. View near the top of Stove Canyon:
Without a 4wd though, it's a long hike in. With a 4wd, it's a good 2 day hike, but you can easily spend 3 days exploring around and there is much to see. With a 4wd and with the trip both to the river and out to the overlook, it's 17 miles round trip, but there are lots of side trips you can take (such as to various overlooks, rock formations, etc.)
Online description of the trail:http://www.utahtrails.com/whitecrack.html
(PS, although not mentioned in the route description, there actually is a hidden spring in Stove Canyon, but you have to know where to look for it; otherwise you have to rely on river water or pack it in).
There are many other good backpacking trips in Island in the Sky as well, but the above is a good one to start with.
I'm slow and fat. Unfortunately, those are my good qualities.