Coronado Cavern, about 45 minutes from Sierra Vista, is nice for hiking, whether you enter the actual cavern or just hike the trails.
Sierra Vista's proximity to Nogales, AZ and Nogales, Mexico makes it easy to cross the border for a quick day trip. Which is how I ended up spending Thanksgiving Day 2002 eating chicken tacos in a little part of Nogales not accustomed to seeing gringos.
My friend Lars and I decided to head down there, what with not having family west of the Mississippi and all, and ended up celebrating Thanksgiving with a couple of shady dudes who latched on to us and tried over the course of an hour or so to sell us everything from drugs to car parts (for Lars' 1971 Volkswagen Thing) to women.
Mainly I think they just wanted to get us in a dark alley so they could club us over the head and take our cash, but we were able to egress the area safely, cross the border, and get back on our way.