From Davis Mtn. you can do a day trip to Balmorhea (by the way, the water is cold), do a day trip to Big Bend Nat'l Park and hike in the Chisos where it's a little cooler. See if there's something in nearby Alpine - perhaps a pool, attend a program at McDonald Observatory - day and night.
You could also break up the week's stay by moving and doing Carlsbad Caverns Nat'l Park - we stay at Brantley Lake State Park. Then an evening program at White Sands Nat'l Monument. Stay in Alamagordo. Just north of Albuquerque is Cochiti Lake Corp of Engineer park and nearby is Kasha-Katuwe Nat'l Monument "Tent Rocks" which is fun for a hike. From the campground it's an easy drive into Santa Fe to explore.
You don't have to spend a whole week in a place. Do other things as you move northward.