I'll second the recommendations for both Mt Lemmon and Saquaro NP. Further north I got some wonderful shots in the White Mountains around the Show Low area. Elk were abundant, lots of meadows and such. A really nice area to shoot considering I was living down in the Sierra Vista area which is primarily all desert. But if you go that far south Carr Canyon is great and there is Huachuca Falls which is a large seasonal falls. Oh, and there is the missionary's church south of Tucson going towards Nogales if me memory serves correctly. Oh and the Patagonia area south of Tucson is nice also. Sorry I can't be more specific but I was only there for a year and left in 1995.

On the bird shots. Most times for BIF try to open up exposure by 1 step to compensate for the dark bird against the light sky. Hawks are about the toughest to shoot but some owls aren't too bad. I'm constantly buzzed by Barn Owls here in Utah that will do repeated fly bys while checking me out. They are the only species I see doing that by have experienced this repeatedly at 3 different locations about 50 miles or more apart. Run up the ISO as high as you can and then set a smaller aperture. This will let you keep the shutter speeds up but will give you more of the bird in focus. It they are against the sky then there's no background to worry about. Oh, but you will find out just how dusty your sensor is, LOL!