Can you even purchase and register a vehicle in the united states without a permanent address? What about insurance on it as well? Will an insurance company insure it without an address as well?
Are you planning to buy something before you get here or just come over and buy something the first day without too much looking? What about when you go to sell it? It could take a month or longer to sell it unless you are willing to lose a good bit of money. While it may end up costing a good bit to rent one, I would rather do it that way and not have the stress or headache of having to buy/sell something, paying for possible repairs, and other associated costs. Another thing to think about is being able to drive.
According to USA.gov...
Short-Term Visitors
If you plan to drive when you visit the United States, check the driving rules in the state(s) you'll be visiting to verify that you can use your non-U.S. driver's license. You should get an International Driving Permit (IDP), which translates the information contained on your official driver's license into 10 languages.
The United States does not issue International Driving Permits to foreign visitors, so you will need to obtain this document in your home country before you travel to the United States.