Unfortunately it is absolutely impossible for you to rent a car if you are younger than 25. You might, if you search wide and far find the odd renter who will deal with you. If so, then the insurance fee will take away any pleasure at all. They "may" charge as much as $ 100 per DAY for insurance in addition to any other costs.

But, why drive in such a car-unfriendly country? The roads are looooong, all look alike, all have THE SAME tired fast food outlets at the stop-overs and are truly booooring to drive. The distances are enormous, don't let yourself be fooled by the small scale on any map.

Get yourself a pass instead, airline passes abound and they are cheaper for students. This is one, but google can help you find several.
The bus-lines cover America everywhere. Buses are slow and not always very comfortable but they are reliable. You will also meet "real Americans" on the buses. Grayline is the largest, but there are many other bus-lines to use. Start here, looking for student passes.

http://www.grayline.com/
There aren't many railroads in USA, compared to Europe, but there are some. Amtrak also sell discounted tourist tickets.

www.amtrak.com

Your "some traveling" will have to be limited in time to the validity of your tourist visa, 3 months. Overstaying is not an option, you may be banned from visiting USA again for years to come when you are found out - at your departure when you hand in your visa as you check in on your return flight.

Need to rent a car in New York? RealCar rental service \ offers luxury SUVs for rent in the New York City area starting at $149 per day. https://realcar.nyc/fleet

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Alex More