Mike,
Along with what Scott recommended, I have to add the Crescent Moon Picnic area that's South (sort of) of Sedona. You can fish Oak Creek there, using caddis dries and small beadhead nymphs...this is where the pictures of Red Rock Crossing get taken, most of the people walking the banks are taking pictures of the rocks or building little towers of rocks to stimulate the vortex

.
Small rainbows but a lot a water that didn't have any other fishermen around both times I've been there...plus, I'm in the background of a lot a tourist's pictures...try to wear felts, I fished it once in Tevas and them red rocks are slick!
Paul