Early December is the end of the rainy season in those areas. The storms tend to be short by that time, but still you will probably get a few quick downpours a week. I’m not an expert on getting around in the Philippines, though I do know that it’s rarely fast or easy. If you want a place to relax then Boracay Island might be the best. Sorry I couldn’t be of more help. -Roger
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 going for one week I wouldn’t go all the way to Thailand, but if it’s two weeks I think it’s worth it. It takes most of a day in each direction, but flights are often reasonably priced, and everything there is cheap once you get there. I’ve actually lived in Thailand for 6 months and have visited many more times and it’s actually very easy and stress free once you are there. All the important signs are in English and nearly everyone you’ll encounter as a tourist will speak enough English to help you as well. You can get around by train or VIP bus for cheap, or fly to the islands for cheap. It’s very safe there as well. You could spend a few days in Bangkok and then head to one of the islands or take a train up to Chiang Mai.
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.
As with other Caribbean resort destinations, the weather in Montego Bay is perfect in December, and the first half of the month is still cheap for flights and resort prices. The weekend before Christmas is when peak season here starts, and if you book early enough you can still get a good deal then, but don't expect many last-minute bargains during that period.
It can still be rainy in Belize in November, so it’s not an ideal time to visit. I quite like Belize and there is a lot to do there, including of course the second largest coral reef in the world. You can also head over the Guatemala border to visit Tikal and even down to Antigua for something different. You don’t get many great beaches there, but aside from that it is great.
All of my best suggestions are in the article above, but I’ll try to expand a bit more. The tricky thing, as you probably know, is that November is part of the heavy rain season in most of Thailand and the other popular southeast Asian countries. There are wet months in summer with just short rain storms, but in November it can often be rainy all day.

Fortunately, Bangkok remains very cheap by almost anyone's standards. If you want to splash down for a nice 3-star room then it'll be half the price of a similar room in Europe or the US, and if you are fine with something more basic then you can find a room for next to nothing, even in the fun Khaosan Road backpacker district. Street meals for around a dollar are always there too, so you'll be able to afford a bit more for a room anyway.

If you book a resort hotel from home you'll probably think Goa hotel prices are much higher than you were expecting, but if you book a family-run place once you arrive you'll still find fantastic bargains. It's probably wise to book a few nights online before you get to India, because it can be incredibly confusing at first. After that you might be able to find a similar place for half the price by just checking around the same area.
Sri Lanka doesn’t really have a good infrastructure for budget travelers at this point. There are loads of nice hotels if you are willing to pay US$40 or more per night, but almost nothing below that except for a few hostels. I haven’t been to Palawan but I have been to Boracay and Palawan can’t be too much cheaper. Boracay doesn’t have many budget options either, so my guess is that Thailand or Cambodia is your best bet.
The subtropical climate of Hong Kong means that summers are particularly hot and wet, and spring is warm and humid. November is the sweet spot, with clear, sunny days and mild temperatures. During your trip, you'll want to take a traditional junk boat ride on the harbour (seen here) and check out the sweeping city views from Victoria Peak, which you can reach by tram. Another can't miss? Stockton, a hidden speakeasy-style whiskey bar in Central.