Not exactly a travelogue

I don't know why this was called Affair in Trinidad, other than a lot of shadows of palm trees and a few sedate dancers, what does it have to do with Trinidad??

All the scenes take place inside buildings that could be anywhere. There's a party scene where Rita does a song and dance, inside someone's house and they all stand around watching her. And they're all dressed up in formal gowns - could be somewhere in Connecticut or New Jersey. Trinidad? Why?