Yeah it sounds like Missouri, Kansas, Kentucky, Tennessee, and Utah would be good for you. A lot of history in some of those states too. Some sights that are touristy but still not "Disney" style touristy that I'd recommend are Silver Dollar City in Missouri, Ark tour in Kentucky, Graceland in Tenn (because it's just a requirement), and Monument Valley in Utah.
For day to day living, I'd maybe do a couch surfing thing?
https://about.couchsurfing.com/about/resource-center/
That'll get you connected with people that are outgoing and friendly. Most people are less so in day to day life so this is a taste without getting a whole plate full of America.
One thing Europeans don't usually think about is in the rural areas of these states guns can be everywhere on good people. In the cities, it's mostly the undesirables that have guns, and they're always hidden.
Back to rural, they might have a holster like a police officer or under their clothes. Don't freak out and call the cops, it's normal like wearing a shirt to them. Know if something happens those guys are friendlies.
Other than that, ask questions. Most everyday people will smile at you and even say Hi. They expect you to smile back and respond in kind. That doesn't mean they want to be best friends, they're just showing that they're friendly. If they say anything more than Hi then they're probably open to answering questions and being in a conversation.
It sounds like you're in for an adventure, and this is probably not a horrible time to do it with elections later this year. Prices are almost double what they were in 2019 (before Covid) so it'll be more expensive right now, but if we change leaders the losing side will probably be looting and crying in the streets again, and tearing up police stations.
As long as you make it here before November you'll pay a higher price but avoid the drama.
Things to avoid (I'm safety minded, I have a family and all that...):
1. Housing neighborhoods with houses under 1000 sq feet. They're usually bad neighborhoods.
2. Big cities after 7pm
3. Any loud people (Yes, I probably mean what you think). You'll get a pass due to the accent, but that pass wears out over time. How much time depends on the intelligence of the Howler.
4. Public transportation (its for the loud people). Take an Uber or drive yourself with a rental.
5. Forests and wooded areas - Not because you'll get murdered, but because of tickborne disease and wild animals that can kill you. If you have a buddy, ignore this. Take tick precautions though.
6. Food off of a truck. It's often delicious, but for Europeans it may give you the mud butt (diarrhea).
7. Untethered dogs or dogs tethered to women. Some dogs are friendly (yay), others are just looking for a reason to rip your throat out. Women will yank their leash and say "omg he just wants to say hi!" meanwhile the dog is barking and slobbering with his eyes locked on your jugular. The dog sometimes wins because it's too powerful for the woman. If you run, bring pepper spray.
I'm sure someone else will chime in with something else, but that's the big things I can think off offhand. Too bad my wife's a xenophobe, or I'd sure put you up here and let you play with Cecilia. My boy's almost grown now and built like a Connor McGreggor, Powder Puff is gone, and just the little blonde is left. We have the room. I'd enjoy the help too. I'm working on building a 3ft x 4ft coffee table from local hardwoods, then taking out a tree that drops too many leaves and threatens me with its ugly face every morning.
Anyway, this has become a small novel so I'll shut up now. Have to take the kids to school anyway!