On the way to Santa Fe is the very large array of radio telescopes which is quite impressive. It's in a MOA but doesn't have any specific airspace restriction. Out of deference I avoided flying through the beam judging by the way they were pointing, lest my Cessna's ignition noise would come up as 'deffo aliens detected' that evening.
Santa Fe is, as said, delightful. It's also very arty - like a giant Sedona.
Talking of aliens, due S of Santa Fe by a couple of hundred miles is the bearded one's
new spaceport. I've no idea if they are accepting visitors but if you claim to be checking it out while passing by in your private plane, why not? I bet you won't be the first.
Regarding Pinal,
Airnav says it's restricted but gives a phone number. It also says the FBO has fuel, so that could be a good enough reason to go there.