Not right on US 380, but south of Carrizozo on US 54 is the BLM Three Rivers Petroglyph Site. It has a half dozen campsites, including 2 with electric and water hookups. Since you are traveling in the fall, I assume you are retired and have a Federal Senior Pass, so the nightly rate with hookups would be $9/night.
The trail through the fantastic array of petroglyphs is not accessible for a person with a walker, but the nearby Mogollon pueblo ruins are. This is the same ancestral Pueblo culture that built the Gila Cliff Dwellings.
And I agree that all three of the pueblo ruins in the Salinas Missions National Monument are easily accessible. However, those are considerably younger (only 1500-1600s!), than the Mogollon sites at Gila Cliff Dwellings and Three Rivers.
If you happen to travel near Santa Fe, you can also visit the accessible ruins at the Pecos National Monument in Glorietta Pass. This is located just off I-25 a few miles east of Santa Fe.