My uncle lives in the southeastern part of the state in a little town called Hurricane, UT. It's right outside St. George. I did a week long trip there last year and loved it.
Just as Snowdog suggested, it would be very near Zion National Park, Bryce Canyon, Canyon Lands, Arches National Park, Moab (my favorite), Goblin Valley & Lake Powell. And a days trip to the Grand Canyon. I haven't seen all of the states yet, but Utah ranks right up there when it comes to scenery.
One caution though. From what my uncle has said, unless you are Mormon, you may find it a little difficult to socialize in Utah. I realize that's a generalized statement, but the way he explained it was that you are considered an outsider. The Mormon people are very polite to him and friendly. But those in his community don't invite him over to dinner as they say. Oh and as a general rule, most don't drink. But with you being there for only a few months, it probably won't be a big deal.
The climate can be tough. On the lower elevations it can go above 100, it is the desert there you know. But you can easily hit a higher elevation in a matter of an hour or two and it will be much cooler.
As was suggested earlier, if you are into motorcycles (off road or street), you would be in a great place. Utah offers a lot of things to see.