Been several years but we stayed at Santa Fe Skies RV park just off I-25 at the southwest edge of Santa Fe. Nothing special but nice enough and easy drive into downtown. And very friendly lady stayed late to welcome us as we had some trouble and was running late.
To see Carlsbad Caverns we stayed at the Carlsbad KOA as reviews for other parks in the area were not impressive. But the KOA is about 20 miles north of the city of Carlsbad and the caverns are about the same distance south. May be better choices now as that was 5 yrs ago. Check rvparkreviews.com.
If you go thru Ruidoso, the Circle B RV Park was very good. And again very nice staff.
About 4 1/2 hrs Santa Fe to Carlsbad. Little more than you planned but not bad.