Trail running in Moab, do you know of any good trails?

As the fall is coming and soon the winter as well, it's time to head to the desert.
I will bring the mountain bike as usual, but this time my running shoes as well...
Do you know of any good hiking trails or mtn bike trails that are nice to run?

I'm not that familiar with the trails down there, and sounds like maybe no one here is ... but of course there are some great trails down there and resources online. Your post did remind me of a 50 miler coming up this month, Moab's Alpine To Slickrock 50...
http://www.backcountryrunner.com/trail-races/alpine-to-slickrock/

So September is still a great time to hit the mountain trails, whether biking or trail running. I hiked Mt Peale in the LaSals some years ago and they're beautiful.