Aside from Indonesia you might also consider Thailand, which has great infrastructure so it’s much easier to travel with young children. Phuket has by far the most options, and its rainy season usually ends in early November. For families I recommend Kata Beach and Karon Beach, which are both just south of the main shopping and nightlife town of Patong Beach.
You could go somewhere that’s cute in December, or you could go somewhere that’s iconic. If you choose the latter, here’s absolutely everything you need to know about traveling to Yellowstone. In brief: There are tons of winter activities (snowmobiling, skiing, etc.), and even though most of the roads will be closed, there’s oversnow transport to get you around the park. Look for wolves at dawn and dusk, watch frost-covered bison plowing through the deep snow, and see the steam rise off Mammoth Hot Springs. If you’re a backcountry camper who knows what they’re doing, permits in wintertime are free.
If you are looking for beach weather in December then most of your list won’t work, and several of them are only on rivers. Starting from Kolkata you have many good choices that are much closer to you than anywhere in Europe or the Canary Islands, or the Caribbean for that matter. In fact, I’m a bit confused by your list because there are so many different types of places on it, many that aren’t warm or on beaches.
The mountains of Canada include the gentle slopes of Mont Tremblant in the east to the towering ones of Whistler in the west. Note that Canadians celebrate their Thanksgiving before the United States does, which makes our neighbor to the north a particularly good place for couples who won't be visiting family during that U.S. holiday—especially if you're willing to forgo turkey and stuffing for crepes and poutine.
We are looking to travel somewhere warm in December of this year, for approximately 3-4 weeks. We are originating from Canada – Alberta, to be exact, and have done a fair bit of travelling throughout our lives, however, we are now bringing along our 4 year old son. With that in mind, I suppose our biggest concerns are now flight durations and safety (in our younger years and without children, these weren’t so much a factor, but definitely are considerations now).
The biggest single highlight in the region is the Angkor Wat temples near Siem Reap in Cambodia. It’s one of the most impressive tourist sights in the entire world, and Siem Reap is a fun and mellow town that you can linger in for a while. Vietnam is really lovely and cheap as well. The food there is excellent, as it’s a fusion of French and traditional Asian. You can go from Ho Chi Minh City in the south on the train to Hoi An near Da Nang, and then up to Hanoi to see Halong Bay. I wouldn’t start in Vietnam because it can be a bit trickier than the others. In the rest of the region it’s easy to book tours and buses and such, but in Vietnam the travel agencies are a bit harder to trust, so you have to be more careful. Things there are very cheap though, so even if you pay more for a reputable agency, it’ll still be cheap.
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.
As Christmas approaches the city will fill up much more, so if you can go early in the month you'll be much better off. But even if you can't go before the last week of the month you'll still find Mexico City to be a tremendous bargain compared to pretty much anywhere else in North America. It's a great shopping destination, and not just for goofy souvenirs, so that's something to think about as well.
Cartagena is a lovely place as well, but another reader just pointed out that the US government has a new travel warning to all of Colombia as of June, 2017. The US has travel warnings to many countries that people still safely travel to every day, but it is something to consider. Many years ago Colombia had quite a few problems, and yet Cartagena was always okay because it is this little cruise port and tourist city far away from the major urban centers. Seeing this, I would think twice myself, although I wouldn’t rule it out, but I also wouldn’t go anywhere except Cartagena at the moment.
Unsurprisingly, the end of December is the beginning of the peak season for resort prices, so those who are able to come earlier in the month will be getting better deals. Still, the all-inclusive resorts are locked in heavy competition all year so this area can be a great deal compared to the alternatives, even in high season. If you are looking for where to go in December for an all-inclusive beach holiday, this is your best option for most people.
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.