Suggestion for Backpacking Trails to Notable Places in the Western US?

If you want to try Az. there are several options. This time of year it's getting pretty warm down on the desert but up here on the Mogollon rim things are just starting to warm up. There are Nat. Forests with lots of accomidations. Old indian ruins to explore. Such as Montazumas Castle. Canyon De Chilly and much more.