We see several post each year about US-54 from the TX border to I-40, and many replies from folks that say it is a good road all the way.
I’ve driven Carrizozo to Alamogordo- very nice road. No real elevation changes.
US-70 is an excellent road from Alamogordo to Las Cruces. Some elevation change as mentioned above. Should be a nice drive for you.
White Sands is an interesting hour or two and accessible for your rig without unhooking.
The White Sands Test Range missile museum at the west end of the valley before the climb out is a full day if you are interested in that type thing. The Museum is open to th bpunlic with ample parking. Military base access rights are not required to visit the museum.
A few miles west of Carrizozo is the BLM Valley of Fires campground. 30 amp with water, nice shower/ restroom and dump station. It is built right on the edge of the lava flow with a great nature trail out into the lava field.
If you are just passing through on one day, eat lunch in Alamogordo because there is no food from there to Las Cruces.