My own experiences "on the other side of the big puddle":

- - Utah. Lots of places to put on your hiking boots and send a selfie from to your friends. Very short autumns and springs. Yes, there are Mormons there. Even in Salt Lake City. But the places where I really felt their presence was in smaller cities, like Logan, Redmond. One experience, especially. At 6' 0' I am not particularly short. One myth prior to going to America that has fallen in Salt Lake City was that I'll feel like a Liliputian in the States. But it nearly came back when I went shopping in the supermarket in one of those smaler cities. Everyone was taller! Literally everyone. The apogeum was at the cashier desk. I looked at the cashier - a teenage girl. Nothing extraordinary. Except she was sitting. And I had to look UP at her

- - Maine. The only autumn comparable in beauty to the Polish Golden Autumn. Except it's red. Not the richest state there is. Probably that's why it's a popular destination for retirement of many Americans. Don't drive too fast on an interstate - moose can kill ya. Not a joke. Really happens. Supposedly the best lobster on earth. Can make a lot of money as a crewman on a half-year long lobster catching commercial cruise. I befriended one local who did. Regularly, he was gone for 6 months. When he returned, he was quite popular because it wasn't unusual for him to buy drinks for everyone. The next month a little more unusual. A couple more months, and he wasn't doing it anymore. After half a year he was again gone fishing. Or lobstering, to be precise.
He was great to talk to, for me, regardless which part of the 6 months away from the waves we are talking about. Not only him. Can't think of one local who wasn't. But it's not a rich state, definitely. Regardless where to look for the reasons. And the shadow of that can be seen in the eyes of big portion of the population, despite the natural beauty of the state.

These two I have spent enough time in to meet people. Of other places I have great memory from:
- - Mesa Verde cliff dwellings monument. Unbelievable how those people managed to live there. How smart they were about making it work. And a thought - how horrible must have been - what they were trying to hide from, there.
- - Seattle. Beautiful city. Don't miss a place with "banistas' - serving free 5000 bananas every day! Compliments of Jeff Bezos. If my source is right about it. Because you won't see any banners "it's from me, Jeff Bezos, make sure you remember that" there.
- - San Francisco. It so happens that I visited it a year ago. Couldn't find the city it was back in the 90's. Everyone is on the move. And everyone differently. A bike, an electric scooter, a taxi with no driver. Probably still there, that place seemingly gone. Probably just need to spend more than one day to still find it.
- - Boston. The city I'd pick to live in in the States, if I had a say. I don't know why. It just seems like a perfect mix of modern and traditional. Or may be it's the memory from the time when I was on a bus, in a traffic jam. Through a window I see a young girl in a car, looking for a spot to park. Not a chance. Wait - here's one! The girl saw it, too, and started positioning for the parking procedure. So happened it was directly across from my seat. No. I was right. Not a chance. To squeeze her car there. Its length matches free space plus or minus a few inches. The girl doesn't seem to realize that and keeps trying. Oh well. She's a young girl, after all - I think. OK. Finally. She's got out of the vehicle and seems to measure the space. Gave me a chance for a deeper level of patronizing tone: She is driving in stilettos! And frankly, made an impression of someone who can perfectly fit in one of the many Boston clubs - but doesn't know how to turn on her computer. Oh boy. What is she doing again?? She waved to a passer by. Also a girl, in stilettos, same impression as the driver girl, on me. The driver girl got in a car, her helper started showing her - this way, stop, a little back now.
10 minutes passed. My bus has moved 2 meters in a traffic jam. In the meantime my jaw dropped. To the floor. The car was ideally parked. I couldn't see a centimeter of free space on either side of it. Two girls. Young girls. In stilettos. Oh, and once the car was parked, before the driver got out to thank the other girl, that one just waved and went her way. A lasting memory, for me. Although not the only one. Futuristic (at that time) flyovers (or whatever they are called), several meters above the ground, from which one can look from his car through the windows of the top floor apartments of old buildings, literally twenty meters away. Well, from the visitor perspective, that one :-D

By the way, I think I'd recommend not having big expectations, prior to the first trip to America. A few of my friends had - and they all returned disappointed after just a few months.
For me it wasn't the first destination I'd have picked for my first destination - behind what had just stopped being the Iron Curtain. But at that time in Poland you went for PhD studies where your former boss at the U had connections. So I went across the Atlantic with a load of myths and preocupations about America and Americans.
I returned to Poland having spent in the US 11 years. Returned without those myths. Just the opposite - with a load of great experiences and great friends I made there. Not saying it's a paradise. It ain't. But it's got a lot of great things to discover. Start with America's well known secrets. But don't stop there. Go on to meet those who live there. Really meet, not just walk among them. Possibly across the spectrum of their backgrounds.
Probably a truism. And not limited to America.

Sorry, kind of long. And not the kind of impressions you will normally look for in travel guides, I am afraid Still, I hope you can find something in it. If not - at least you will know where not to go ;-)
Blame it on the fact that I left the States 25 years ago, return to Poland. Two visits, since then. But only a few weeks long.

ps. Nice one, about the SW shirt in your post Go Sheffield! Except when you play Tractor Boys :-P

Just one more place, may be more to your liking.

- - Newport Beach, California. The widest beach I've ever seen. White sand. Big waves. And NO PEOPLE! Ok, there were two, other than me and my girls. The rescue team.
I don't know, may be it was just on that day. But it seemed strange. Or may be the reason was different. The city itself is not a tourist destination. It's a city with a large marina and seemingly very expensive yachts. No clubs, no fast food. Anyway, it was 15 years ago, so may be it's changed since.

And one more experience from Maine

- - "Renegades" bar, don't rememeber the town's name, and the name of the place must have changed, if not closed, because I can't google it. Close to Bar Harbor (that's where you can eat a fresh lobster, though I don't). But you can probably find similar atmosphere in other places away from the common tourist tracks in Maine. So here's a warning - don't be fooled by ads about the friendly atmosphere and local climate. Better check before going. In my case it was a deadly combo. Yes, it was friendly. But not for me. I drove 100 miles from Orono where I lived, because the restaurant ran an ad in yellow pages that it has a pool table. They had a place with many pool tables closer to me, in Bangor, but when I went there alone, I spent the whole time playing myself. It was crowded, but ppl came with their own groups of friends. There was one where I used to play, in Old Town, and it was great but I wanted to try a new surroundings.
Now, the bars like that in Maine, are not just bars. They have a bar, and a dance floor. The pool table is extra. And on weekends they have a dancing, but not the way I usually think of a dancing. Guys in cowboy hats, gals in cowboy boots, country music and country style dancing. It was the same in Old Town, so I got on a car, grabbed a check book and a bunch of quarter coins for the pool table - and off I go.
I got a beer, put the quarters to enter the queue, and sat at the table. After the first game I returned to my seat. A guy comes to sit next to me. After a few minutes he asks me what's my name. And why I came here. My name's Peter. To play the pool, I answered, expecting a conversation with a local, something I am really looking for.
And he then says: Mister Peter. You students have your own places. Don't come here. Do you understand what I mean? And looks in my eyes. I think I did. I noticed a few strong looking guys waiting anxiously what my reply will be. And nobody's face gave any sign that they'd help me. I panicked. Jesus, I didn't even look at your ladies (the first thing came to my mind, what I did wrong)! So I tried to convince him that I _really_ came only to play pool! He let me finish, and said - You seem a nice guy, mister Peter. Play one more game and leave. Take my advice. . It was then when I recalled a bar in Orono, a boy, blonde hair, angel face, whom I saw for the first time there. When we got to talk, he told me he didn't come from Bangor to dance with girls. He came to take one to his room. And the serious expression on his face when he was saying that, was a striking contrast with a smiley face when he was dancing.
So I didn't argue with the guy at Renegades. Played one more game, said a thank you, and left. Glanced at the door when I was ten meters outside. Just in case :-D
Not trying to scare anyone. Just a warning. The ads in Yellow Pages were probably run by some "Renegades" chain. Definitely not by the person who I got in a little chat with there. :-D

As said, never was in the US. Just know what I did see in documentations and other TV stuff.

But if Cities are more enjoyable for you, I think Chicago would be a place to be for you. It has almost everything, including Art, Sports, Nature, Architecture.

Smaller places might be San Francisco, Portland and Seattle.

Also the East-Coast-Places are interesting I think, so Boston and Philadelphia as example.

Also interesting could be a more college driven community, if you like sports. Like Louisville, Memphis or Salt Lake City.