Road-trip in USA: can a foreigner buy a car?

Yes, anyone legally in the US can buy and register a car. I have several European and Australian friends that own and keep motorhomes here even though they are not citizens. Some Canadians do the same thing. The only time Canadians get in trouble is if they try to take the vehicle across the Canadian border. Canada gets on their case and forces them to register the vehicle in Canada. Insurance requirements vary from state to state. Most states require proof of insurance to get license plates. I think your biggest problem will be deciding on what states to register the car in. At that point, you will need to check with that state DMV on exactly what their requirements are. I had an Australian friend that bought a motorhome and got a 60 day temporary driveaway permit. He drove it for something less than 60 days and used his Australian address as the new location where the vehicle would be titled and licensed. After the 50 or so days that he sold it in the US and never titled it himself in any US state. He did get US insurance for the time he drove it here. I do not know about taking it across the US Mexico or US Canada border. I do not think I would try it.

People visiting on a tourist visa will have no problem buying a car.

Registration and insurance are more difficult.

(Full disclosure: my company, visitor.us, helps international visitors buy, register, and insure vehicles as an alternative to renting.)

Vehicle registration is regulated by the 50 US states, so there are 50 sets of registration laws.

Some states, like Tennessee, require proof of residency in the state to register a car, while others, like Georgia, require an in-state driver's license.

We published a Free Guide that covers the international visitor's vehicle purchase, registration, and insurance process for 20 of the most frequently visited US states. I hope it's a helpful resource for you and your trip.

In order to register a car in any state, you will need an address there. You can use a friend's house, but I would be careful about using an AirBnB address: once registered, you'll need insurance, and as of 2019, most insurance companies are doing an additional layer of vetting on applications for policies with an address that's also a short-term rental. I.e., you'll need to prove you live there to get a policy.

Would some dealership sell to you? Probably. Would the state allow you to register and insure? Much less likely. Most, if not all, states would require a local address for registration and many require insurance, which again is likely going to require a local address.

You'd need to check individual state government web sites to determine if any would allow this. For example, http://www.state.nj.us/nj/trans/

Unlikely to get insurance. You are most likely going to take more than a $1000 dollar hit when you buy a car, what if it breaks down? Think about: Who is going to buy this car, how long will it take to find a buyer? You may need to file taxes. Lastly there is significant paperwork for selling a car, which means DMV visits. It may be cheaper to rent...