In Central America you could consider Belize. It’s small, but it’s got islands and beaches (not everywhere though) and forests and other cultural sights, and English is more or less the official language. It’s not as well organized as Costa Rica, but it’s not bad and it feels safe. The other to consider there is Panama, which obviously has a lot in common with Costa Rica. It has far fewer adventure activities and the good beaches are spaced out a bit, but still it’s a relatively rich country with tens of thousands of Americans and Canadians living there as well as visiting, so they have a good tourist infrastructure and it’s safe.
Still, this is a perfect time of year to find bargains, as the full-on busy season doesn't begin until mid December. You might have to stay a few blocks off the main tourist strip if you are looking for something in a backpacker price range, but fortunately there are still plenty of very cheap restaurants and bars all over the city if you scan the menus carefully.
If you crave warmth but think the beach bores you, head to the Southwestern United States. New Age meets Old West in Santa Fe, Phoenix is still toasty and its cultural season is in full swing, and Denver makes for a great trip. And if you've never seen the Grand Canyon, winter is a good time to visit since the crowds have thinned out (but do dress warmly).
One of the best things about Puerto Vallarta is that, unlike most of the Caribbean destinations, this is a real historic town rather than a purpose-built resort community. That means that there are small and authentic (and cheap) restaurants catering primarily to locals, so you get a much more authentic experience if you prefer one. The hotel zone close to the airport is modern and posh, but you are a short taxi ride away from the lovely center of town.
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.
Actually, most of the popular European cities have fairly mild winters, in that they don’t spend much time below freezing and snowstorms are rare as well. It’s hard to make suggestions without knowing about your tastes, but I will tell you that the most popular European cities are London, Paris, and Rome, and none of them get snowed in often. If you are going to Italy, you should also go to Florence and maybe Venice as well.
In South America, and you start getting into some longer flights here, the best and safest places are Argentina, Peru, and Chile. I’m not sure if this helps you much, but at least it should let you know that you were thinking along the right lines already, and there are no obvious places that you’d overlooked. Let me know if you have any other questions. -Roger
Austria Salzburg, Vienna Belgium Bruges, Brussels Bosnia and Herzegovina Sarajevo Bulgaria Sofia Croatia Dubrovnik, Split, Zagreb Czechia Cesky Krumlov, Prague Denmark Copenhagen Estonia Tallinn Finland Helsinki France Lyon, Nice, Paris Germany Berlin, Hamburg, Munich Greece Athens, Mykonos, Rhodes, Santorini Hungary Budapest Iceland Reykjavik Ireland Dublin, Galway Italy Florence, Milan, Naples, Rome, Sorrento, Venice Latvia Riga Lithuania Vilnius

If you’ve got 5 to 7 days and are starting in India I don’t think you want to fly halfway around the world, so it’s probably best to go somewhere between Dubai and Bali. Dubai has cheap flights from most places and it’s very family oriented with large play parks inside shopping malls and that sort of thing. You could get an apartment there in one of the many apartment-hotels for a reasonable price, and the December weather should be pretty good as well.
Cancun is at the north end of the Riviera Maya, which also includes the island of Cozumel, so this is a huge area with over a thousand hotels to choose from. All that competition keeps prices down until the high season begins, so November is still a buyer's market. There are even ruins nearby and other cultural opportunities, so it's not all about sitting on the beach here. If you prefer a high-rise hotel overlooking a beach then stay in Cancun itself, but if you prefer to stay in a friendly town with many restaurant and shopping choices then head to Playa del Carmen, just a bit to the south, instead. 

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 Keto Diet works best if you can maintain it. If your body is continually switching from converting carbs to glucose, instead of converting fat to ketones for energy (which is the process of ketosis, wherein the liver converts fat cells into energy), your weight loss will possibly stall. Consequently, you may find that some health benefits of eating a Keto-friendly diet begin to diminish. Find a healthy balance on your next vacation; with some planning, you can maintain your Keto Diet even when you are out of your routine.
But again, Vietnam can be a bit complicated for first-timers. Specifically, you need to book trains and tours through travel agencies, and Vietnam’s many travel agencies have a worldwide reputation for being hard to trust. They are all great salespeople but the product they deliver isn’t always what you expected. I spent 4 months in Vietnam and loved most of it, though I think it was much easier as a solo traveler who didn’t have a set schedule.

Hmmm…this is a tricky one. Since you want to get out of SEA, you might have to go a long way to reach someplace that could be considered cheap and also has decent weather in December. Japan and South Korea will be cold, and not really cheap. If you go south you hit Australia, which is very expensive by most SEA standards (although not bad by Singapore standards). Perth is obviously closest and it’s a real city, and of course Sydney and Melbourne will be in early summer in December so those could work if your budget allows. Brisbane and Cairns are both known for outdoor activities, although nightlife might be tough for teenagers and there are no real cultural sights.
I’ll be happy to give you some suggestions, but it would really help to know your starting point and approximate budget. At this moment I am writing this reply from Cancun, which could be perfect if you are in or near the US, but if you are in another part of the world there will likely be better choices. Although thinking about it, even if you are in Europe, a place like Cancun might still be best. Let me know and I’ll give you my best answer and an alternative or two. -Roger
If you can, try to stay at a hotel or hostel that has a kitchen which guests are allowed to use. You can also elect to find home-share style lodgings, as people often rent out their homes during peak vacation times for tourists to use. Once you have a kitchen, you have control over what you purchase and what you eat. An added benefit of this style of travel, other than the fact that you can stick to your Keto Diet effectively, is that you get to experience the local side of life. Going to grocery stores, choosing from local ingredients, and cooking for yourself will help make you feel like you’re a part of the culture, instead of only a visitor.
Orlando’s theme parks are a major draw for families (and big kids, too!), but this iconic experience doesn’t necessarily come cheap. During the pre-Christmas November lull, however, hotels often offer attractive discounted rates, meaning potential savings and – more importantly for the kids – less time spent standing in line. Those looking for a more alternative American adventure should consider the island of Puerto Rico in November. While there’s a chance of rain (but a greater chance of balmy beach-lounging days), the out-of-season discounts are as appetising as the island’s take on Thanksgiving dinner: turkey stuffed with mashed plantain.
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