If the Caribbean sounds better, I’ll recommend Puerto Rico. The area around San Juan is fairly crowded, although not nearly as crowded as a typical resort area that is loaded with hotels. And there are many smaller resort towns on other parts of the island where people usually rent a condo for a week or two. In a town like Rincon you won’t get crowds, and you will get great beaches.
In colder weather it’s probably better to focus on the great cities rather than places more known for scenery and outdoor activities. If your budget is generous then my top choice would be London, Paris, and Amsterdam. You could fly into any of those and then visit the others by high-speed train. The train that connects London to Paris and Amsterdam is called the Eurostar, and the earlier you buy your tickets the cheaper they will be. Paris and Amsterdam are linked by normal high-speed trains, which are also cheapest when you buy early. Speaking of that, your dates are prime travel dates over the Christmas holidays so the airfares will be kind of expensive and they will only go up from here. In other words, buy as soon as you can.
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.
Trekking in Nepal during peak season might not sound like the most sensible choice for penny-pinching backpackers. But you can still enjoy the ideal weather without spending a fortune on in-demand hotels and expensive permits if you're happy to swap big-name trails, like Everest Base Camp and the Annapurna Circuit, for quieter treks to Kanchenjunga Base Camp and around the Langtang Valley. Idyllic conditions (dry but not witheringly hot) are also on offer in Rajasthan, one of India’s most vibrant and varied states. Chug between notable, attraction-rich cities like Jaipur, Jodhpur and Udaipur on an atmospheric and wallet-friendly Indian train, snacking on spicy pakoras and sipping sugary chai en route.