Alamogordo is kind in the middle of where I would travel. Depending upon where you come from with 28 days to spend:
From the east - Exit I-10 in San Antonio and travel US-90 to Marathon and BBNP
Night 1-2 - Seminole Canyon SP - 30A
Night 3-7 - Big Bend NP - 50A/FHU
Night 8 - Big Bend Ranch SP - Dry
Night 9-11 - Davis Mtns SP - 30A or 50A FHU
Night 12 - Balmorhea SP - 50A
Night 13-14 - Guadalupe Mountains NP - Pine Springs CG - Dry
Night 15-17 - Carlsbad Caverns NP (Carlsbad KOA is a great CG - White City RV - no so great) - FHU commercial parks - Brantley Lake SP has some electric sites - just be aware that there are no good quality RV camping locations close to the Caverns.
Night - 18-20 - Oliver Lee Memorial SP (Drive over the mtns via US-82 is interesting with a steep descent to Alamogordo - if those type grades bother you go north to Roswell and take US-70 over the mtns
Night 21 - Valley of Fire BLM CG - 30A just west of Carrizozo (US-54/US-380 intersection) camp on the edge of a lava flow - alt is 3 Rivers Petroglyphs Site a little east of Santa Rosa - 50A - a great hike enroute to Carrizozo from OLM SP)
Night 22-23 - Elephant Butte Reservior SP - Many electric sites
Night 24-28 - Deming, NM - Rock Hound SP has several electric sites as a good base for the area. City of Rocks SP to the north has some electric sites - not the best sites in the park. We base at the Escapee's Dreamcatcher RV in Deming.
If coming from the west, I'd reverse the route.
Full-Time 2014 - ????
โNot all who wander are lost.โ
"You were supposed to turn back at the last street."
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2014 Flagstaff 832IKBS TT