If you just want to get in the air, check out the view, and experience the local procedures, you don't need a licence at all. You simply book a flying lesson with an instructor.
I have flown in many random locations that way, and providing you have no hangups about the fact that there will be an instructor in the right seat it is a great way to fly new and different aircraft types, and fly in some interesting places.
For many years I made a point of "type collecting" whilst on business trips, and on that basis I would suggest that you should NOT be looking for a school that rents generic Cessnas. Since aircraft hire in the USA is generally much cheaper than in the UK, I recommend that you take the amount of money you would normally spend in the UK on an hour in a C172, convert it to dollars, and phone a few flying schools and ask them what they will rent you for that amount of money. You might find a Mooney, or a Bonanza, or even a twin. Or how about a float plane, or a tail dragger, or whatever. I'm sure you get the idea. There's no chance of getting signed off solo in any of these machines, but who cares? You're on vacation!