If you are looking for parks near Bosque del Apache NWR, there are two. We have stayed at Bosque Birdwatchers and the other--Chupadero Mountain View--is just north of it on NM Highway 1. Birdwatchers is much larger, but Bill is very difficult to contact by phone. So just go there without reservations, pull into an empty FHU space, and set up. Bill will come and collect the $25/per night from you.
The nearest campground to Socorro at Elephant Butte State Park is the South Monticello cg. It has very long, 30/50A electric sites, water, a dump, and a new solar restroom-shower building, for $14/night, including the daily park pass. However, it is ~50 miles from BdA and 65 miles from Socorro.
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