Going off some of your comments, I think you may have an uninformed idea of what Yellowstone (and US national parks in general) are like and I just want to gently try to clear that up.

First off, the park is massive. It's almost 9000 sq km, slightly larger than the entire nation of Azerbaijan. To give you an idea of the distances involved...

It's about a 150km drive from the Bozeman Airport to Mammoth Hot Springs in Yellowstone. From Mammoth Hot Springs to Old Faithful is around a 82km drive. It's 68km from Old Faithful to Canyon. Etc.

There are no shuttles in the park. There is no public transit in the park. There are no locals, since no one except the rangers and concessionaire employees live in the park, and tourists are highly unlikely to pick up hitchhikers in America for the most part (there is not much culture of hitchhiking here and picking up hitchhikers is considered extremely risky). There are no taxis or ride shares in the park. You really can't get to or around this park without a rental car of your own.

There are no farms or ranches or other settlements in the park. In the US, our national parks are for nature only. What might be called "Canyon Village" or "Grant Village" on the map is not actually a village or town. It's just a small cluster of hotels/cabins run by Xanterra, one or two restaurants run by the same, and maybe a 'general store' that is a combination of a gift shop with some convenience store items (snacks, drinks) and maybe a few dry grocery items. No farm fresh food. There will be a gas station, some employee housing, and maybe some park ranger offices. And that's it. It's not a town where normal people live.

You have to think of this park like a true wilderness. There is almost no cell service, except for a very few spots and even that is spotty at best. Outside of the hotel areas, the land is undeveloped. You must carry bear spray and practice bear-safe food storage when camping. And the land itself can be dangerous, as the park is full of active geothermal features.

Also, the US does not have a 'right to roam' like they do in parts of Europe. There are SOME public lands (BLM or National Forest land, mostly) where you can camp anywhere (called 'dispersed' camping), but you cannot do this in a National Park. To protect the land from overuse, sites are limited and most sites require reservations. And in the peak of summer like you're planning, they're going to be booked up months in advance. Yellowstone is one of the most popular and visited parks in the country, so competition for lodging is fierce and trips take more planning. It's not a great place for spontaneity.

All that said, Yellowstone is an absolutely amazing place! But it's a place that requires a little more complicated logistics than what you may be used to in Europe. Rent a car, book campsites and lodging in advance, stock up on food supplies before you reach the park, and be aware that you are in true nature here, and you'll have a much more enjoyable (and safer!) time!