If you take your dog to the Jemez it's not problem. I think every where you go here in NM its dog friendly as long as you clean after it you should be ok. I don't anything about the other states but NM is animal, nature friendly and accommodations for them and their owers.
Try calling the Cochiti Visitor Center. They had info on this park and the surrounding area and they may be able to tell you a place you could board your dog for the day. We did see a veteranian's office in the town of Cochiti Lake that might help.
No dogs allowed in Tent Rocks
I was just there in May, they do not allow dogs at the Tent Rocks Park. Service animals only. My brother had to turn around and find a friend keep his dog so we could go.
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