I have a bunch of options for you. If you were scuba divers you'd have lots to do in any of these. If you like to snorkel and are comfortable with it then scuba is easy. Do your classroom and pool work in Calgary while you can take your time and then do your open water dives in the warm Caribbean.
I'll start with places you wouldn't think of when you say Caribbean.
Belize: think Mexico but more English as it was a British colony. You can stay on Ambergris Caye where most tourists go or on the mainland to Placencia or Hopkins/Dangriga area. Lots of non beach things to do: hiking in Jaguar national park, a bunch of different Mayan sites to see, cave tubing, the Belize zoo. We did a fun snorkel trip in Ambergris where you also caught some fish for a lunch BBQ. Then there are beaches. Diving options abound, and it has many top class dive sites along the second largest barrier reef in the world. For a small country there is a lot to do. Plus getting there wouldn't be tough. Easy from here to Texas and then a bunch of flight options or you might be able to go Westjet to Cancun and then a flight from there.
Honduras, specifically Roatan: great for diving, our favourite dive resort is there. Some nice beaches, but not a lot of other things to do. The mainland is sketchy but the Bay Islands are safe. Fly to Houston/Dallas and then it's about a 2 hour flight.
Panama: other than causing you to sing Van Halen, it has a lot of varied activities. Panama City gives you urban while the outer areas like Bocas Del Toro give you beach and ocean. You can aalso go inland to Bocquette (sp) for hikes. We dove in Bocas, it was ok. Another Calgary - Houston/Dallas flight.
Costa Rica: I'm reaching here as most activity is Pacific side but it has a ton of different things for you to do: watch turtles laying eggs, visit the rain forest, see a volcano. It has all inclusives, and used to have, and I'm assuming still does have, charters from here.
Traditional Caribbean
Puerto Rico: You can spend a couple days wandering around Old San Juan. You can then go to Culebra and or Vieques and get some beach and snorkeling in. Culebra has long empty beaches you can wander for hours. At certain times of the year in Vieques you can kayak when there is phosphorescence in the water. Every disturbance in the water would cause a light show. That would give you a mix of city/urban and beach. Diving there was ok. We went through Chicago I think but pick a US hub.
Turks and Caicos: Great scuba, lots of beach, not much else if you want to do other things. I think we went through Miami.
Dutch ABC islands
Aruba: a large stretch of the island is a national park giving you hiking options. It has some pirate caves to see, wild exposed beaches, and towns where you can get nightlife if that's your thing. Diving was surprisingly good. We went Calgary, Newark, Aruba overnighting in Newark both ways. You can go through Toronto if you really want to.
Bonaire: I think everyone on the island is there for diving, ignore it of you don't.
Curaçao: The most populous of the ABCs with the most infrastructure. I have not been personally but have a sister and family who aren't all day every day beach people and they were happy with their week there. I think there are all inclusives there or at least Euro plans. I believe there are charters from Toronto.
...and I'll say it. Going to Cuba and spending part of it in Havana before the Americans wreck it would be a good option.
Have fun wherever you end up.
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