Moab is a town in Utah.
Pretty easy to get from I-70 down to Moab. While winding and scenic highway 128 follows the Colorado River through epic canyons, it is less traveled and therefore a tougher hitch than 191. Easy enough to thumb out of town in any direction.
128 is definitely worth seeing, possibly one of the most breath taking roads out there. There are also many camp sites along the river. For 'free' camping try Sandy Beach around mile 12-13 and the 'nude beach' around mile 5. It's possible to stay out there for days at a time, and easy to hitch back and forth between town. Where 128 splits off from the 191 going out of town there is a natural mountain spring - just a few hundred feet up on the right side - with some of the best water around. The locals claim it will make someone fall in love with you =)
In Moab, the library has free internet and is a good place to chill out during the blazing summer days. There used to be a FNB style feed called FreeMeal, not sure if it still exsists. If so, around noon in front of the library you can grub out for free and meet locals. If you have to sleep rough in the city of Moab, I suggest the basketball court near the library. There is a gymnasium next to the courts with an underground staircase that provides discrete shelter. But really, you'd be better off hiking out of town and into the desert. Moonflower Canyon is rad.