Mexico, Cuba and Venezuela you can literally go to those places and feel like a king with less than $500 but those countries are dangerous tho.
Cuba is not dangerous at all, but Americans need to go to Mexico first and get a permit at the Cuban embassy so their passport isn't "tainted". Not sure if the Obama administration relaxed this, but Americans used to have a hard time getting there.
Mexico itself is OK, just don't do stupid things like going to bad places with unknown people at night etc, and don't look rich.
In Venezuela thanks to the magic of hyperinflation, you can indeed feel like a wealthy person. Unfortunately criminals believe the same thing and you become a walking target, not just for mugging, kidnapping and ransom is common and widespread under the lax socialist regime who is all too busy imprisoning political dissidents to care about actual crime.
It is actually dangerous to enter the country with more than about 500 USD, you can become target in the airport itself. There is a case of someone from Egypt that made the mistake of declaring bringing more than 10k USD to customs (which is what the rules say you should), apparently someone from customs or someone from inside the airport's ("secure" area) was involved with a criminal gang and gave the info, the guy was gunned down at an exit gate to steal his money. The video was shared in youtube,
