I suggested Tucson and then I was curious so I tried to price it out:
$605 direct on SWA to PHX x 6 = $3630
Minivan rental $780
Vrbo (lots of different price points, but here's one -- you could probably do better than this but it has a pool, mountain views and is only $300/night) -- total $3782
https://www.vrbo.com/3758184?chkin=2024-12-27&chkout=2025-01-05&d1=2024-12-27&d2=2025-01-05&startDate=2024-12-27&endDate=2025-01-05&x_pwa=1&rfrr=HSR&pwa_ts=1723244276006&referrerUrl=aHR0cHM6Ly93d3cudnJiby5jb20vSG90ZWwtU2VhcmNo&useRewards=false&adults=2&children=1_13%2C1_15%2C1_16%2C1_17®ionId=553248635976475171&destination=The%20Foothills%2C%20Tucson%2C%20Arizona%2C%20United%20States%20of%20America&destType=BOUNDING_BOX&neighborhoodId=553248635974904701&latLong=32.33445%2C-110.92015&nightly_price=217%2C600&privacyTrackingState=CAN_TRACK&searchId=a473cdcd-c0b7-4be3-9a3e-4c421df0d7f4&sort=RECOMMENDED&top_dp=300&top_cur=USD&userIntent=&selectedRoomType=100982615&selectedRatePlan=0004ddb36aa575414fa9a791c6da1de4e082&expediaPropertyId=100982615&propertyName=Mountain%20view%20home%20with%20private%20pool%2C%20tranquil%20patio%20%26%20beautiful%20kitchen
For activities I would do:
Saguaro National Park
Sabino Canyon National Forest (there's a nice tram that goes up the canyon and then you can hike as you please, or another hike from the visitor's center that goes to waterfalls)
Sonoran Desert Museum
Day trip to Karchner Caverns and Bisbee and/or Tombstone (take the mine tour in Bisbee!)
Maybe day trip to Biosphere if they have it all open again
Pima Air & Space Museum
Maybe Titan Missal Silo Museum
Horseback riding
Maybe Old Tucson (watch the Stunt show!)
San Xavier Mission (get the fry bread and shop in the excellent jewelry and gift store)
Maybe walking or bike tour of the historic downtown Barrio
There might also be Christmas-y type things to enjoy
If your budget is tight, I would add up the prices of these things and then decide if you want to spend more or less on the house. I think the Desert Museum is the priciest of the things I listed, or horseback riding--many of the others are pretty cheap.
I bet you could do something similar for someplace like Santa Fe or other places in the Southwest. It's not going to be really warm (it's a little random with the weather at that time of year), but it will be pleasant and there's a lot to do.