You may want to look into getting an
International Drivers Permit. It's not required for UK drivers with a valid license, but can be handy for insurance purposes or to convince an uninformed cop that you have a legitimate right to drive.
This is definitely good advice--if nothing else, it makes you look like you've done your homework and care. When my nephew was here from Japan driving my car he got one first, and my insurance agent was fine with him driving under those circumstances.
Also, when you rent the car, you should make sure that the agreement you sign includes permission to drive in whatever states you plan on visiting. It shouldn't increase the price at all, but the agreement will have specific permitted locations and not bringing it up in advance could cost you if something bad were to happen in a state not on the agreement.
For example, I rented a car from Hertz in Chicago, Illinois and got included on the agreement permission--at no cost, and with no particular hassle--to drive in Ohio, Michigan, New York, and Canada (I was driving through Canada as a shortcut to get to Niagara Falls). You just need to ask.
If you're doing back roads also check the fine print on the agreement if it prohibits certain places--there are often a few very specific exceptions (usually very bad dirt roads in isolated places--Alaska, for example), and since I think most rental cars have logging GPS units now they could well ding you for taking it somewhere you weren't supposed to even if nothing goes wrong.
Funny note on out-of-state license plates: I'm in California, and in addition to the common Oregon, Washington, Alaska, New York, Rhode Island, etc plates, I've actually seen Hawaii license plates on more than one occasion. How the heck does that happen?