Since you are stopping for Carlsbad Caverns you should at least drive the 45 or so miles down the road and stop at the Guadalupe Mountains NP Visitor center and perhaps walk thru the Frijole Ranch site. Guadalupe Peak is the highest point in TX and quite impressive to see.
The general consensus for camping near Carlsbad is the KOA north of town or perhaps Brantley Lake SP. There are other in the area but not that great.
Road conditions in the area are good but it is HOT, Highs 100+ expected all this week.