I've traveled pretty much around the world and have been to over half the world's countries. Since you said you wanted to stay in the Western Hemisphere (North and South America) I'd ask you one basic question: What do you want to do in your vacation? For example.
1. If you want to party till you drop: Buenos Aires. BA is Paris, London and Barcelona put together, a party atmosphere in an elegant city, perhaps even more elegant than New York. With a very LGBT accepting vibe. Argentina has had LGBT equality since the 1850s , and was the second country in the Americas to have full marriage equality throughout the 1 million square miles of its territory. Great people who like to have a good time, dance, more clubs than most large American cities. Amazing wine country. Spectacular architecture, good mass transit. Downside: 13 million people, so if you're looking to leave New York's hustle and bustle... nahhh.... And the diet. Argentines are about the most meat-eating country on the face of the earth - not a good place for Vegans. Also what may be an irritant: Porteños (people in Buenos Aires) eat and play at inordinately late times, 9 or 10 PM and then clubs open at 1 AM until the morning. If you're an early riser, you're in the wrong place.
2. If you want nature in an accepting environment with lots of relaxation: Costa Rica. Commonly called the Switzerland of the Americas. Volcanoes, natural parks galore, UNESCO biospheres, world-class beaches, high living standards compared with the rest of Central America, easy to get to from the East Coast. Your money goes a long way in Costa Rica. Downside: Although very accepting of LGBT, "Ticos" are generally conservative in their personal habits, even LGBT people there tend to be low-key. Not a big party scene if you're looking for one.
3. If you want beach, beach, beach and scuba in a totally "Do your Thing": Any of the ABC islands, Aruba, Bonaire, Curacao. Former Dutch colonies and still tied to the Motherland politically, they are an LGBT heaven with a live-let-live vibe. Especially Curacao, where most hotels are IGLTA members and court gay travelers aggressively. Tremendous food - especially seafood. A few Gay clubs where you'll feel at home. Willemistad, the small capital, is a gem, a World Heritage site. The ABC islands are off the Venezuelan coast. They also are outside the Hurricane Belt, so even during "rainy" season the sun shines. Downside: A little hard getting to. And if you're looking for the bustle of South Beach, you won't find it. It is a place to relax, party a bit, and have a wonderful vacation.
4. If you want to ski while North American summer rages: Chile. Some of the best ski areas anywhere. Portillo is self-contained. The three conjoined areas 8,000 feet above Santiago, La Parva, Nevados and Farellones, offer world-class skiing, bowls and amazing views of the 22,000 foot mountains around it. Chile also has amazing wine country like its neighbor Argentina. There are amazing views in some of the national parks to the South of Chile, Torres del Paine among them. Downside: Chile is the only Latin American country that is considered "First World" and has the prices to match. Their standard of living is not unlike the US. Santiago, the capital, has nice architecture but busy and smoggy.
5. If you want one of the most historical places on the planet: Cartagena, Colombia. Besides beautiful beaches, in the outskirts, the city is a UN Patrimony of Humanity. Staying in one of the old convents turned hotels is an amazing experience. Cartagena was the seat of the Spanish Main, the old Vice Royalty of the Spanish Empire and it has architectural jewels unseen anywhere else.
6) If you're looking for the world's capital of biodiversity: Ecuador's Galapagos Islands. Only problem is that all visitors must be accompanied by a guide as Ecuador is extremely jealous of its number one national park. As a result, it is quite expensive and scheduling a tour must be done in advance.
Places that I considered nice but I wouldn't go again: 1) Rio. It's a huge city and although very LGBT friendly, the concerns about personal security, pickpockets, high prices and the fact that the city is being torn apart for the World Soccer Cup and the upcoming Olympics is a downer. Copacabana and Ipanema are great beaches for people watching and admiring gorgeous men, but after a rainstorm, both beaches are polluted with raw sewage. 2) Caracas. The entire country of Venezuela has gone to hell in a handbasket. Caracas used to be a world-class gem but is now filthy, crime ridden and unmaintained. Angel's Falls is a world class treasure but getting there you have to take one of the Venezuelan airliners and I wouldn't ride on one of their planes if you paid me.