If you can manage a couple of days or so, there is a lot to see and do in southeastern Arizona.
In addition to the above suggestions, which are all very, very good, there is Ramsey Canyon just outside Sierra Vista with a ton of hummingbirds.
If you are interested in heading over to see the cranes or Cochise, etc., you could set up in Willcox, which is the home of Rex Allen, the cowboy movie star.
At the north end of the Chiricahua Mountains is old Fort Bowie, which was used as the base for campaigns against the Apaches, plus a Butterfield Stage station. You would have to hike a bit over 3 miles to get there. It should not be bad, if you are coming during the fall, winter or spring.
However if you are coming during the winter, keep an eye on the weather. The high country in SE Arizona can get some nasty storms.