You mentioned no kids, no grandkids. That simplifies things, but may also leave you without practical supports that family can provide in retirement. So while you're looking for "middle of nowhere" also consider something of a local community (even if small) you can be involved in, in some way, so that you have some options for friends to talk to, people to call in an emergency, etc. Also consider how/where either of you might want to live when one of you eventually passes. Do either of you have siblings or other extended family that live in a place that would interest you? You could explore your options near them while visiting family.
I have extended family members that moved to a lovely remote spot, then complained that the extended family didn't visit them often enough. It was a very long drive away for the rest of us (nowhere near an airport, train station, etc) and visits were infrequent. I think they would have been happy with visits once a year or so, but it was more than could be managed for most. The experience ended up being sadly much more isolating for the wife than the husband, as he was more of a loner than she. And now that they are much older, health care has become very complicated. Things like needing to wait a month or so for a specialist to come through the small town that is an hour or two away, or making a many hour trip to a bigger city. (Is that unusual recent vision change an eye problem or a stroke? Well, neuro will pass through in 3 weeks an hour away, ophtho will be here in 6 weeks...) Eventually, one 80+ year old person that probably shouldn't be driving long distances anymore, driving the 80+ year old seriously ill spouse to appointments far away, etc. They moved far from their kids who could have helped them and been a bigger part of their lives in their old age. Beautiful place, though. I'm not sure if they have regrets, or not, perhaps they think it was worth it. But it has been difficult for family to watch from a distance, and be unable to help them. You won't have kids worrying about you, but you may face similar struggles.
If you can afford two home bases, as some others have suggested, that might be a good option. We have friends who have done that, and enjoyed their retirement split between two places they like but that have different advantages (weather, medical access, near old friends, etc). And now as they are getting older they can pick the place that suits their needs better now, and let the other place go. This can be done by purchasing two places, or buying in one area and doing long vacations in the other (rentals, RV, etc). Another option might be to keep one home base and add an RV and travel a lot to different areas you'd enjoy. You could enjoy the western states, while avoiding wildfires by picking up and driving away, for instance.
Just some ideas. Hope you find the right place for the two of you.