We just went back at Easter this year for the first time! We stayed in what looks like the same place as 01tj and it was a nice place, pretty close to most things and only a couple of miles south of town. When you get to town buy a book with all the trails and that gives all the information you need. I can't remember the name of the book at this moment but they sell them at at several places in town. Also, ask questions! The locals were super nice and helpful when we were there! As for time, we stayed seven full days and only scratched the surface! We took five very capable rigs/ drivers and covered a lot of ground but never got in a hurry or tried to rush the experience. We hit all the big names and some of my favorites were Prichet's Canyon, Clifhanger, Moab Rim Trail, Poison Spider Mesa, Golden Spike, Hell's Revenge and the hot tubs! We also hit Kane Creek which is very different type of trail for out there. It is a sandy creek bed trail that sits in a valley with water running through it that is nice, but it is so dusty to get to the creek that I could have missed it and not been all that disappointed! Then Potato Salad is only about 2 miles out of town and draws a crowd every afternoon and makes a good place to stop and play some more! On the last day we hit Rusty Nail and it was awesome!
All of these trail heads are not far from town and will take 5-6 hours to enjoy and take in the scenery! Some will take a little longer but we would eat breakfast every morning and leave out of town about 10am and not get back until 7-8pm each day. It was the most awesome week I have ever spent in a Jeep!
Good luck and enjoy!