Maybe consider Rapid City, SD. I think the population is about 75k. It’s on the interstate if you want to easily travel to other places. It’s right next to the Black Hills and Wyoming if you want to have hiking/camping/wilderness nearby. Also not too far from Colorado if you want to travel down there. There’s plenty of smaller towns around there if you want to live in a smaller town but have a nearby city to do shopping. I think it fits the low population, semi-rural but still around people, good place to “survive” (wilderness, animals, rivers), and livestock (lots of ranches - my best friend works on a ranch 20 miles south of there) requirements.
@dchris mentioned Sioux Falls, which is a nice city but it’s probably like 200k. Probably getting to be like 1/4 of South Dakota’s population in that one town. I do like it there, though. It’s got nice features.
Look at some Minnesota towns - Duluth, Bemidji. I don’t know the population of Rochester but I’ve heard nice things. Mayo Clinic is there, if anyone in your family has any chronic or unusual health issues. And I know it’s not what you’re looking for but I think the Twin Cities are one of the best metropolitan areas in the country. Super green for such a large place, and lots of educational/cultural/fun opportunities for kids. I go a few times a year and always find cool things for my family to do that we can’t experience at home.
I like the Sheridan, WY area but I’ve heard from locals it’s getting hard to afford.
Missoula, MT is also very nice. Probably getting hard to afford as well.
Montana, Wyoming, western South Dakota will have mountains, more genuine wilderness, and animals. Some decent sized rivers, depending on where you are. A little further east will get you more lakes, forests (not that there’s no trees in the other states, but they’re not as forested) and quality farmland, if timber and good soil are features you would value in the future. And rural areas still have plenty of animals. I think NE S.D. has what is considered some of the best soil in the country, for now… modern farming practices are slowly destroying everything that made it good in the first place.
These are all northern Midwest. That’s what I’m most familiar with.
If you want to avoid people, stay between the Rockies and the Mississippi.

EDIT: Another thought occurred, as I see what’s happening in NC. I live close to where SD, ND, and MN meet. The worst weather I experience is extreme blizzards and occasionally-colder-than-Antarctica temperatures (seriously).
And every few years a tornado might come through, but I’ve never actually known someone who’s been affected by one.
There’s no hurricanes, no tsunamis, no earthquakes, no wildfires that destroy entire towns… basically, there’s almost never weather events that would displace you or that one couldn’t, with some thinking, be prepared for. You can hunker down during a blizzard. You’re not going to lose your house like you might in a fire or a hurricane.