37.7804° N, 25.4970° W
Halfway between North America and Europe are a cluster of islands, the Azores. Until recently, there weren't direct flights out of the US over there. I was able to catch the first one over. I think I'd want to spend longer than 5 days there to explore more of the island and its neighboring tourstops. A quick 4-hour flight from New York and you feel like you are in a truly exotic part of the world.
One of the highlights of my trip was the abandoned hotel in Sete Cidades. I am not sure how much longer it will be left standing but wandering through an abandoned hotel with a breathtaking view from the roof is something I won't soon forget.
Ponta Delgada is the touristy part of the island, there are the usual array of clubs and bars. It was kind of dead when we were there, I think if you make to this part of the world you'd be better off experiencing nature and the unique sites anyways.