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New Mexico Museum of Space History in Alamagordo was pretty neat 30 years ago....haven't been back in the area since.
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I was there a few months ago. If anything, it's even better than when I went there 20 or so years ago!
ETA Almagordo is 2 hours each way to/from Socorro.
About 73 miles south of Socorro is Truth or Consequences, which hosts several establishments with natural hot springs. There are some
museums there. I have only visited the Geronimo Springs Museum, which was pretty interesting.
If you have the urge to visit the UFO museum in Roswell... pass it up. Totally hokey. Unless you are really,
really into that kind of thing.
Just be prepared for LOTS of driving! New Mexico consists of miles and miles of nothin' but miles and miles! So bring along some in-car entertainment for your child.
And of course, standard emergency car stuff. LOTS of water, broad-brimmed hats (the NM sun is merciless), water, tools, water, sunblock, and water. Also, be prepared for long stretches of road that have no cell phone service.
It's very easy to become dehydrated. And since much of NM is above 5000 feet, altitude sickness is a real possibility... which will be exacerbated by dehydration. So bring water flavoring stuff that you and your child will enjoy.
If you are going to Trinity, there are a number of sites to visit so plan your day accordingly. Study the site and get as much info as you can.
Truthfully... VLA plus Trinity are a day's visit. VLA is interesting: there's a self-guided tour around the site, plus a visitor's center and gift shop. The visitor's center has a movie theater displaying info about VLA and the science surrounding it.
Socorro is the home of New Mexico's Institute of Mining and Technology; they have a very limited-access* museum there.
Have Fun!
* only open for very restricted hours.