Being from Mumbai you can be forgiven for not realizing how unappealing beach areas are when the air temperatures are only a bit above freezing. Seriously, even beach on the European mainland is totally deserted by November 1, and many of the local hotels and restaurants are closed by then until April or so. Now, if you are mainly after the novelty of being on a beach in the European winter, you can certainly go and still find open hotels and restaurants. If I had to recommend one place to consider it would be Spain’s Costa del Sol, which is the resort area around Malaga. The average high in December in Malaga is 17, and the average low is 8. You’d be the only one on the beach, which might be kind of nice. It’ll also probably be windy. If you were going to do that I’d recommend staying in Malaga itself, which does have a nice beach area in the city, and since it’s a city the hotels and restaurants will all be going.
As for Costa Rica, I think it would be ideal for what you have in mind. It’s by far the most tourist-friendly (and English speaking friendly) country in that area, so it’s a great starting point. Belize is pretty easy as well, although there is far less nature to enjoy. Panama and Nicaragua are a bit cheaper and have similar things to offer, but Costa Rica has the best infrastructure and nature parks, so it’s less stressful for a first-timer. The snorkeling is better on the Caribbean coast, I believe, but the better tourist beaches are on the Pacific. The country is pretty quick to get across, so you could easily spend a few days on both sides, plus another few exploring the rain forests and volcanoes and such.
Vietnam might fit the bill for what you are looking for. The most popular itineraries are to start in Hanoi and end up in Ho Chi Minh City, or the other way around. There is a nice train connecting them that is scenic in many places, and the best must-stop place in between them is Hoi An. You also don’t want to miss Halong Bay, which is just outside Hanoi. Vietnam mostly attracts cultural travelers rather than party people. The food is excellent (France used to run the place) and there is plenty of culture all around, in addition to some nice beaches in Nha Trang and Da Nang (next to Hoi An).
The rainy season in Cartagena winds down by early November, so this is an ideal time to come, especially toward the end of the month if you can get cheap airfare before and/or after Thanksgiving. The temperatures are pretty much the same here every day of the year, so the key is to work around the autumn rainy season to when it's dry but before hotels fill up.
Lovers of historic architecture should consider tiny Malta in November, which still basks in glorious warm weather as much of Europe starts to shiver. The baroque palaces, churches and fortifications of its harbour-hugging capital Valletta look much the same as they did 400 years ago, and are extra lovely when observed from a traditional dghajsa (open boat) water taxi. If a life on the high seas has always appealed, then charter a course for the Cayman Islands come November, when the serene Caribbean isle hosts Pirate Week, a fun-filled festival that includes costume contests, street dancing and a horde of swashbucklers ‘invading’ the island and capturing the governor.
It’s unfortunate and heartbreaking how many times I have recommended San Juan, Puerto Rico in the last few years. Once they get the power back on I’m sure it’ll be back to normal fairly soon after that, but I’m guessing probably March or later. And fortunately, Nate missed the Cancun area for the most part. Have you considered somewhere in the Cancun/Playa del Carmen/Cozumel area? I’m particularly fond of Playa del Carmen, and that flight to Cancun should be pretty reasonable for you.
If you’re a fan of cheese, this place is really fun. It’s a quaint little shop that’s right across the street from Pike’s Place Market. With hundreds of competitive awards under their belt over the last decade, you know their cheese is going to be good – and they do too. They let you sample different varieties of cheese before you buy it, so you know exactly what you’re getting into.
You’ve got a pretty good budget so you can afford to go almost anywhere, assuming you are okay with renting one or two houses or villas instead of 4 hotel rooms. If you are willing to fly all the way to Asia, your best bets would be Bali or one of the Thai islands, probably Ko Samui or Phuket. In all of those places you should be able to rent a house or villa near the beach and then do activities and day trips very easily.
If you’re a bit more on the timid side, you can always use Yelp and TripAdvisor to get good insights on places people have visited. As a disclaimer, some of the ratings may not be accurate on these sites, so make sure you go through and read some of the more recent reviews that people have written. We did this for a few of the places we visited and had no issues.