Take a drive South of town aways to State Route 211 and head into the Needles District of Canyonlands. Goto the Visitor's Center (not the outpost) and take the dirt road to the SW of the BLDG (it says 4x4 only, or something like that). Take it to the very end, something like 4 miles. Doesn't seem like much, but you will have to use your four wheel drive and creep (stock VX will do fine here). When you get to the end, walk to the edge. AMAZING views of Salt Creek and The Colorado River. This spot is indicative of what Canyonlands is all about; however, there is sooooo much more to see.
The above would be a good side trail to do along with Elephant Hill. Note - This would pretty much be an all day affair.
Dead Horse Point has a great view (no wheeling needed)
A nice all day drive to see this part of the country is: Moab South to the LaSal Junction (SR 46)(turns to 90 in Colorado) to 141 into Naturita, Co. Continue 141 through Slickrock, CO, onto HWY 491 just West of Dove Creek, CO. Head West, back into Utah, into Montecello, UT, then North on 191 back to Moab.