Great Moab trails that will give you a really good time without the OMG, I could die factor:
1. Dead Horse Point State Park. 9 mile loop suitable for a novice, but still great fun for an advanced rider. Superb, unique geography and scenery. Can do quickly and still have time and energy for another ride.
2. The Brands Trails--have every level of difficulty and you can custom tailor a route in the nicely stacked loop system to your liking. Start with EZ or Lazy and then head to Deadman's Ridge if you want some really fun, flowy, moderately techy stuff. If you want more miles, then add on Bar B, Circle O, etc. UtahMountainBiking.com has the best descriptions of these trails.
3. The whole Klondike Bluffs/Baby Steps area is pretty good and theres also the opportunity to custom build a route to your liking. This is a busy area, especially with Jeeps in the Klondike Bluffs area, which surprisingly adds to the fun (and the safety factor).
4. Of course, there's also Slickrock. The main loop is a fairly strenuous 10 miles, but that's the one trail in Moab where you're truly never alone. You'll have fellow riders every inch of the way.