I just got back from 2 weeks in CO and UT... dropped down to AZ for my buddy to see the Grand Canyon. For us, even 160, 163 and southern parts of 191 were scenic. For an early EASY trail and possibly camping spot, check out the Valley of the Gods trail. Take 163 through Mexican Hat and turn left onto 261. Around 6.5 miles up the road there is a turn-off for the trail. It's more of a dirt road than a trail (when the wash crossings aren't washed out, a high-clearance car can do it) but a good first spot to get your tires dirty. Watch for off-shoot trails for a lunch or camping spot. No vault toilets though... When you're done, the trail exits onto 163, turn left to continue the trip.
There are a lot of fun trails out there that you can safely do solo (well, depending on your trail experience). I used the Moab trails book from Wells. I'd recommend picking it up, if you haven't already. http://www.funtreks.com/index.php?Itemid=32
These are the trails I ran (2.5" spring lift, lockers and 33s)...
Sevenmile Rim (including Wipeout Hill) a few off-camber spots, but not bad. You can go down the rocky side of Wipeout Hill and up the slickrock side fairly easily. Consider adding Tusher Tunnel to this trail for a cool scenic thing.
Hells Revenge (including Hells Gate).. not recommended if off-camber scares you, do not try Hells Gate alone. For a much easier experience, try Fins and Things. I ran that last year with a stock Rubi and didn't need the lockers.
Top of the World. lots of big ledges... worse on the left side of the trail after it splits (recommend taking the right part of the loop going up and again when you come back down). This trail is 30 miles from town. If you get an early start, you can do this with Dome Plateau, but it'll probably be too long.
Dome Plateau is a nice moderate trail, nothing super challenging... towards the end you'll see two old mining cabins. Across from the second cabin is a walking trail that leads you to an old stone storage room on the canyon wall. Walk downhill from that and the next level down has a few short mines (100 feet in, but bring a flashlight). When you finish the trail, 3.3 miles down the road south of the exit point is a faint turn-off for an old cave home. I don't know anything about it, it appears to have been used in the mid 20th century, judging from the quality of the cinder block walls.
Poison Spider Mesa... a few challenging rocky climbs (and descents since it's an out-and-back trail) but with good spotting you can do it. Still, not recommended for most people running solo. I would recommend against taking the cut-off for the Golden Spike trail (which leads to Gold Bar Rim) when running solo. I didn't even try.
inside Canyonlands NP, Needles district (south of town, take Rt 211 from 191 and stop off at Newspaper Rock for a cool photo before continuing to the park)
Colorado River Overlook... starts from the visitor center, a fairly easy trail for a lifted Jeep but a great view. Combine this with Elephant Hill for a full day.
Elephant Hill... a bit harder than the overlook trail, but was fine for me. There's one switchback where they want you to reverse down a leg because it's too tight for some longer vehicles to turn. I took the trail to the Confluence Overlook and hiked out to see it, then drove back. An option is to continue down the trail to a few trails deeper into the desert but they wash out frequently.
We also did the White Rim Trail, but it's a 2-day trail when done correctly and not challenging (4x4 vans do it all the time when supporting mountain bikers). But, you could take the Schafer trail down the switchbacks from the main road inside Canyonlands NP, Island in the Sky district (uses the same 7-day vehicle pass from Needles district) and follow the trail to the Musselmann Arch, then backtrack and take the Schafer trail to Potash Rd back to town. Or take it reverse direction if you want to climb the switchbacks.
For camping, there are some free "dispersed" campsites in the area, but no toilets. I think you're required to bring a portable toilet if you camp in dispersed areas there. There are a bunch of fee sites on BLM land that do have vault toilets, though. A bunch down Hwy 128 (the road down the canyon towards Top of the World trail). Sand Flats Recreation Area (home to Fins and Things and Hells Revenge) has a ton of fee campsites with vault toilets... $10/night. We stayed there for 3 or 4 nights.
If you do want to do the White Rim trail and decide to camp, reserve the Murphy Hogback camp site "A". Amazing view... we climbed on top of the big rock and slept under the stars. Had set up the tent right near the cliff with a wonderful view from the tent door, but didn't even use it.
Also, take the turnoff for "White Crack" and hike out to the point. You'll have a 270* or better view of the canyons if you can make it all the way to the point (there's a spot you have to jump down and climb a little).
To add to the adventure, don't skip Arches NP, it's right outside town and the famous Delicate Arch is a 90 minute walk from the parking lot. We did it at night for photography, but day time is a much easier hike and you can actually see it.
Sorry for the long post, just wanted to share my experiences... it's an awesome place.