Be sure to read Chapter 5 of Abbey's Desert Solitaire. It gives a good Ranger's-eye-view of what it feels like to be descended upon by visitors (though he didn't face near the number of visitors that modern rangers do). Ask questions other than "where's the bathroom" and "where is the coke machine" if you can. They'll particularly appreciate knowing you've done your homework and want clarification or recommendations of how to really enjoy their park.
These days in Indian Country you'll often see signs telling you if residents don't want you to photograph in their community, or stating the restrictions. DON'T assume that if there is no sign, it is okay. Resist the urge to travel down a twisting driveway to visit a lone hogan. Outsiders are not entitled to see what's around the corner of a rutted road that leaves the pavement, or in any way trespassing. It's just as if you wouldn't want someone walking in your yard or front door and photographing you.
If you want someplace to visit in the early part of the year, Southern Arizona is the place. By May the Sonoran desert is already too hot for most visitors, but February through April are delightful. Watch to see if they get good rains this fall, that determines how spectacular the flower displays will be next spring.