Yeah, in the park borders you can't ride except on paved roads. As for south of the park itself, as has already come up a guide is your friend. But remember that Flagstaff is just a quick drive down the road and the riding there is supposed to kick ass. It's on the list for a fall visit for us.
You might also call a couple of shops in Flagstaff. In my experience, they're all pretty helpful and can get you pointed in the right direction. I can't suggest one over the other, but google will get you some numbers.