Happy,
I, like most herpers, generally plan my annual excursions to that great state to coincide with the monsoon season (July-Sept.). May and June can be very hot and dry (but with this year's El Nino weather pattern, who knows?). Depending upon the day to day weather, the higher elevations can even become unproductively cool at that time of year.
It seems that you are familiar with some of AZ's herp regulations, but remember that their definition of "take" (i.e., requiring a license) can be interpreted to include photography, especially if it involves a listed species. My advice would be to "bite the bullet" and purchase the expensive "Non-Resident Hunting License" to cover yourself. That, however, only includes reptiles; for amphibians you will need an additional "Non-Resident Fishing License" -- I know, go figure, but that's the law. Depending on the length of your stay, a somewhat cheaper three-day version of these licenses is available. I believe both can still be purchased through the AZGF website. Collecting is not really much of a problem if you have a license, as most non-listed species have reasonable bag limits.
Although some herpers have recently perceived an anti-hobbiest bias on the site in general, the AZ PARC Forum [http://p206.ezboard.com/freptilesofarizonafrm1] contains helpful observations from actual field herpers on the scene. As far as specific locales, there are too many to begin to list and, of course, it depends on what you are looking for.
Good luck.
Tom Lott