Hi Jill,
I'd recommend Arizona in either March-April-May or Sept-Oct in terms of the best time to go, although everyone's opinion will vary. I'm sure you're well aware that the summer months can get a little warm. The winter months can get a little chilly/snowy for camping, depending on where you are, but I don't think it's anything you wouldn't be able to handle if you're an experienced camper.
As for where, I've only been once, and to one place, and I loved it. So I'll throw a vote out for
Oak Creek Canyon in Coconino National Forest (Sedona). Great hiking and greater views. If you don't have a camera borrow one!