ooh I wouldn't fancy NEPA -- have lived near Philadelphia and NEPA is old school coal country and quite depressed.
If I wanted more rural and could choose anywhere it would be somewhere like the Hudson Valley between New York City and Albany, further up enough to get the price down. It is gorgeous. The mountains aren't the Alps; the Appalachian chain is geologically ancient! But it's beautiful low mountains with tons of trees, the river, cute towns. Politically quite mixed but state government leans liberal. The Finger Lakes are also beautiful (the slogan is "Ithaca is Gorges") but the weather there is challenging. There is a snow belt across central and western New York that makes it one of the snowiest places in North America. It has to do with the direction of lake effect winds off Lakes Erie and Ontario. Buffalo and Rochester get more snow than Toronto because of it and the areas inland even more. Some rural areas get hundreds of inches a year.
I love Maine, especially towards the coast, but Portland is pricey. We live near DC and every year right around July I start saying we should move to Maine for the cooler weather. But we never have...
An area like this would also give you access to city things including health care. One issue with living places in the US that are really rural is that health care, especially specialist health care, is hard to access. The Mountain West is exceptionally bad. If you are in Montana or Wyoming (which are also very conservative, aside from somewhere like Missoula which is a college town) you will need to travel to Denver, Salt Lake, or sometimes even Seattle for health care. For many decades, until perhaps 10 years ago, the only medical schools (and hence comprehensive academic medical centres) in the Northwest were in Seattle and Portland.
In the Northeast the sort of town you want to watch for is a place that has de-industrialised and is now depressed: those are the towns that are ground zero for opioids. Vermont is classically New England pretty, but I do think this would be a shock. It was big news when Vermont got its first Target store 5 years ago!
Also only the coastal PNW is mild and green (parts are a temperate rainforest). Once you go east of the Cascades you are in a rain shadow and it is steppe and desert, with ribbons of greenery along some of the rivers.
The Rockies are beautiful. However they are not lush like the East Coast because it's so much drier. The forests in the Rockies are evergreens, and you won't see all the vegetation you see in forests here. Also, because of skiing and vacation homes, the economies of many towns in the mountains are really lopsided. In the famous CO ski towns there's nothing under a million and all the service workers are priced out.
Charlottesville is a lovely college town and there are a lot of nearby small towns in the Blue Ridge.
Yes, the culture is different but as someone who moved from the UK to the US (albeit with American relatives) it also varies massively from place to place. People on MN act like everyone here is a Charlie Church with a gun especially outside a few big cities but it's much more complicated than that. Be aware that really rural places may not have good internet service.
I do think you should visit before committing to such a big change!