How long do you inted to stay in Moab? There are so many trails there, to do all of them would take you weeks! That being said, since you're going solo and may not be familiar with what it's like to drive on slickrock, I'd stick with some of the easier (difficulty 3 or lower) trails.

Klondike Bluffs may be a nice trail to try. You'll probably enjoy going through Arches NP.