Hey Jimbo,
I'm like you, I don't live in NH or WY. I'm trying to decide when/if I should move. I've been to NE Wyoming as well as western SD and it's nice. I have relatives who live in western WY and I'm a big college sports fan so I'm thinking carefully. Good luck in what ever you choose.
The last thing I'd want to do is discourage a prospective mover but I will share why I didn't end up going to NH,
Number one was the distance from the west, To far from familiarity & family.
2) Population density of the East coast & Nuclear plants.

3) Property Taxes and prices. (High)
I've been accused of being paranoid, I prefer to look as it as paying attention but any kind of societal collapse major world wide disaster or serious war and New Hampshire is not where I want to be, there's no escape by land if there's any type of massive civil unrest which I give a high probability in mine or my childrens lifetime, I believe sooner than later.
I went to a few festivals out in NH I really enjoyed myself, the people are great for someone not as catastrophe minded as myself you might not find it as unsuitable.The population density of Wyoming is very attractive, my current dilemma with it as a candidate is the Off-grid house I've designed is entirely based around a desert climate and Wyomings climate will require a lot of modification. (Solar powered & earth bermed.)
We move out tomorrow, First to Oregon for a brief stay with relatives Then our routes Idaho, Wyoming, Utah, then North Arizona settling on the best prospect.