Why not both? You can easily fly into one spot, drive around to the cool spots and fly back from another. And if you haven't been to Santa Fe that means you probably haven't been to the rest of New Mexico either. And other than Hawaii and Utah, New Mexico tops my list of best state for road trips and hiking. Plus it's probably my favorite state/regional cuisine after Cajun and New Orleans Creole, even ahead of Florribean, Low Country and Californian.
If you drive in to New Mexico, you can hike the dunes of White Sands
Hike around Valley of Fires
Hike the Slot Canyons and plateaus of Tent Rocks
Hike the Sandia Crest which looms over Albuquerque
Go to Taos to see the oldest occupied building in America several thousands of years old plus hike, hunt and fish
Do hikes throughout Carlsbad Caverns which is the best cave system in the US, much more scenic than Mammoth in Kentucky and far bigger than Luray in Virginia, it's almost on par with Jenolan in Australia or Waitomo Glowworm Caverns in New Zealand
Also in addition to the spots in New Mexico (those I mentioned plus other things like Shiprock and/or Roswell you can easily stop off at on a driving trip), there's a fair amount in Southern Colorado to do that most people flying into Denver to do the Rockies never see.
I HIGHLY recommend Great Sand Dune National Park and Durango
I'd suggest flying into El Paso and then flying back from Colorado Springs (and no I'm not suggesting a full Tribe trip, last time I did New Mexico, I started in Biloxi went through New Orleans and Cajun country then into Houston, dipped down to Big Bend National Park then up through Marfa through to Roswell, Carlsbad and White Sands, then up through Albuquerque, Santa Fe and Taos then all over Southern Colorado before exiting out of Colorado Springs, then darting across Kansas to KC then down to Fort Smith Arkansas to visit my in-laws then across Little Rock to Memphis and then down through Birmingham to get back to Tally. We did that over two weeks, so you could easily do the NM and Southern Colorado portion in a week.