We normally boondock but Brantley Lake SP worked for us when we wanted amenities.
If you're in reasonably good shape, the Lower Cave tour is a great addition to your Caverns visit.
For us, other points of interest in the Carlsbad area include
the zoo http://www.emnrd.state.nm.us/SPD/livingdesertstatepark.html
Sitting Bull Falls http://www.fs.usda.gov/recarea/lincoln/recarea/?recid=34238
Dog Canyon http://www.fs.usda.gov/recarea/lincoln/recarea/?recid=34238
McKittrick Canyon http://www.fs.usda.gov/recarea/lincoln/recarea/?recid=34238
and driving the FS roads in Lincoln National Forest
