My brother and I have done this a couple of times.
First was in 1992 - hired a 182 RG out of North Carolina - at the time my brother was a 56hr total time PPL with no complex (me no PPL at all).
He did a check out in the airplane (N9888C - I recall, saw the airplane for sale in bits a few years back) - it cost US$45/hr dry - we flew up the rivers in New York, Niagara Falls, Oshkosh, out to Boulder in Colorado and a host of places in between - it was about three weeks in total.
Second trip was out of Florida 1994 - another 182 RG out of Orlando Executive - we just walked in the door and rented it - did Key West, Bahamas, a two week trip - the flight to the US was a freebie - remember the Hoover Flights scandal
Third time was to Las Vegas - 1996 - hired a 172 RG Cutlass - again just walked in off the street at North Las Vegas airport - flew the Grand Canyon, around the edge of Area 51, Hoover Dam, Death Valley.
My brother lost his medical in 2000 so that stopped those trips - so maybe post-"9/11" things are more difficult, but I do not think so.
The first trip we had lined up the airplane before we got to the US (very complicated in the pre-Internet days) - the others we simply walked in off the the street and selected one of several nice looking airplanes with a company name of it and then went to find their office.
I would think the same thing would apply now, but with the internet it would be simpler - I would also suggest placing an advert on Barnstormers.com with you requirements and see what comes out of the woodwork as an option too.
If anyone wants to fly the Eastern Caribbean and has an FAA PPL and 100 hours my newly refurbished Archer II is available for rent - lots of interesting islands down here, not too long to fly to them
The Grenadines are rather spectacular, 45 mins flying from Barbados to Bequia, Union, Canouan, Grenada, Tobago, St. Vincent, St. Lucia etc. all within 15 to 90 minutes. Oddly commercial it costs more to fly from Barbados to Bequia than it does to fly to New York so if you want somewhere that makes Barbados seem like the heaving metropolis, get to the Grenadines!