Congratulations. In order to help you I’d have to know your starting point and also whether you are more interested in cities and culture or beaches and relaxation. November is a tricky month for beaches since it’s a very rainy month in most of the best and cheapest beach areas and islands in the Northern Hemisphere. But if you give me a bit more info I will try to help you the best I can. -Roger
One reason that Vietnam isn’t as popular as it could be is that travelers often feel a bit hounded when they are there. For some reason, those in the travel business in Vietnam (working at travel agencies where you book tours and such) make tourists feel like they are being hustled. They are rarely 100% honest with what they tell you or about the prices they are charging. Still, it’s an amazing country and it’s also incredibly cheap, even if you end up paying a bit more than you were supposed to. I highly recommend it, and it won’t be a problem if you realize before you get there that you can’t take everything at face value in the way that you usually can in Thailand or Bali. Quality of hotels for the money is also very good.
Preheat oven to 425 degrees. Line a rimmed baking pan with a sheet of parchment paper. In a medium bowl, toss the green beans, garlic and olive oil together until completely coated. Then, spread the coated green beans on the lined pan in a single layer without crowding. Season with salt and pepper, then roast in the pre-heated oven for 15 minutes. Remove from oven once during this time to turn the beans so they cook evenly. When finished roasting, remove from oven and place beans on serving tray. Before serving, drizzle with extra virgin olive oil and sprinkle with grated Parmesan cheese. This makes a great recipe for Thanksgiving dinner sides.
The “city that never sleeps” is a delight in December, even if the weather makes it necessary to bundle up a bit. For holiday spirit and things to do any time of year, New York City is a top destination. Broadway and off-Broadway shows are exceptional entertainment, and the Radio City Music Hall Christmas Spectacular with the famous Rockettes is a perfect holiday event. The New York City Ballet at Lincoln Center presents the classic "Nutcracker," a seasonal tradition. At the New York Botanical Garden, the toy train will wind its way through a miniature Lower Manhattan for the amusement of kids as well as nostalgic adults who may have once had their own train sets. The dazzling Rockefeller Center Christmas Tree, New York City’s centerpiece each year with nearly 50,000 lights, will once again overlook the famed ice skating rink and golden Prometheus statue. Window shopping takes on new meaning during December when department stores along Fifth Avenue entertain passers-by with intricate decorations and displays. Holiday markets at Bryant Park, Columbus Circle, and Union Square also invite browsing and shopping along with warm drinks and food. For a convenient stay, the Renaissance New York Midtown Hotel offers spectacular views and Versa, a year-round rooftop restaurant and bar. Or enjoy the Innside by Melia New York in the trendy Chelsea area with its newly opened seafood-focused dining spot, The Wilson.
Those temples are all outdoor for the most part, so cooler and dryer conditions mean you can spend more time touring the temples and still being comfortable. Almost any other month of the year and you'll be better off going back to your hotel for a few hours in the afternoon, but in December you can carry on all day if you like. The town of Siem Reap is a delight in itself, but of course it fills up near Christmas.
If you are referring to days trips and that sort of thing, it will be much cheaper if you book once you get there. In Vietnam in particular it’s amazing how cheap tours can be if you book them through your hotel. I once did a 6-hour bus tour to Mỹ Sơn, which is near Hoi An, and I think I paid about US$6. It even included a boat ride and a basic lunch. That same day tour online would probably cost US$30 because the booking company takes a share and there is very little competition.
Aside from that, this is a bit tricky because you obviously want to avoid longer flights for a short trip and especially with an infant. And some of the closer options are not close to a major airport, so they are still hard to reach in half a day or so. I think if you want to go farther than Goa, it’s probably best to look for other options in Thailand. As you know from previous visits, Thailand really has tourism figured out and it feels safe and well organized there. Cambodia and Vietnam also have beaches, but none that I’d recommend for a short trip. It’s the same with the Philippines, and the flights start getting longer. Phuket is the largest Thai island by far and it’s got over a dozen different beach areas and towns to choose from. Patong Beach is the main beach town and I wouldn’t recommend it for a family, but Kata and Karon beaches are just south of that, and they are nicely family oriented. Phuket also has a large airport, so getting there quickly is pretty easy compared to other beaches and islands in the area. Phuket’s beaches are also very nice. I wish I had more suggestions for you. Let me know if you have any other questions. -Roger
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.
Prices go up a bit when you go south into Malaysia, but it’s worth it if you’ve got the money. You might even consider Myanmar as well, which I’ve yet to visit, but I keep hearing great things about. It’s honestly the perfect time of year there. By April it’s insanely hot (the hottest month of the year), but December through February is lovely. It’s all quite safe as well, as long as you keep your wits about you. I’m happy to help with more information if you need it.
It would be hard to beat Chiang Mai for its combination of great November weather and low prices. Even though it's officially the start of the high season for hotels, the beginning of the month is usually very slow anyway, so bargains are common. Hotels in Chiang Mai are among the best bargains in the entire world, so even if you do have to pay full price for a room it'll be cheaper than a dorm bed in most European cities.
I’m happy to help. As mentioned above, November is a very tricky time for a sunshine holiday because so many of the better places have their rainiest season then. I agree about the DR. It’s an excellent place for big all-inclusive beach hotels, but outside the hotels there isn’t much of interest unless you are fluent in Spanish and hopefully know a local. One you might consider is San Juan, Puerto Rico combined with some stops elsewhere on the island. November is part of the rainy season there as well, but I don’t think it rains all day very often. And the city of San Juan is excellent for nightlife and things to do, so even if you get a couple rainy days you should be able to find some things to do. By then it’ll be over a year since the hurricane and San Juan has already been close to normal for a while now. There is still some damage, but it would be easy to avoid.

Your December plans probably seemed fine until this very moment when you realized they didn’t yet include Reveillon on Copacabana beach -- one of the biggest and best New Year’s Eve parties anywhere in the world. December is summertime here, so you can spend your trip under illuminated palm trees on the beach, before joining two million (yes) other humans for the debauchery of Reveillon. To extend the trip, join a week-long tour that gives you a blend of rainforest, city, and beach.

Late October (when the rains end) through February is an exceptional time to visit the northern part of the country, from Sukhothai through Chiang Mai and Chiang Rai. The King’s Birthday, on December 5, ushers in the festive season (Christmas and New Year’s certainly aren’t traditional holidays here, but many Thais celebrate them anyway) and cooler, less humid weather. In general, the beaches are blissful from the end of December through March. Mid-November through January see the lowest temperatures and least humidity in Bangkok.
From November through February there are literally no European cities that could qualify as having “great weather.” We list Tenerife below because it's technically in Europe, although not really much of a cultural destination. Antalya, Turkey (which technically isn't even in Europe), has the closest thing to a sunny climate with acceptable temperatures. So during the winter Europe is all about cultural tourism, and lower hotel prices make it especially appealing for those who like to stretch their travel budgets and avoid crowds at the same time.

If you decide to go off keto whilst you’re on holidays that’s ok. There are two ways to approach this. Give yourself a cheat day or cheat meal or go totally off for the entire holiday. I would prefer a cheat meal over a cheat day or cheat holiday simply because I know that one meal, while it may switch me from burning ketones to burning sugar, won’t make me feel too bad. I know if I have a cheat day or a whole cheat holiday then I feel sluggish, tired and won’t enjoy myself. It’s a personal choice but if you do decide to leave keto at home while you are on vacation don’t berate yourself for doing so. You’ve got a solid foundation on keto, especially if you’ve been keto for a while, so switching back on when you get home won’t be too painful. However, if you think that it will be a slippery slope to a total carbfest then maybe try to stick with keto. It can be done! If you have any tips or tricks for staying keto on vacation make sure to leave it in the comments. Knowledge is power and the more we share the better we get!
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. 
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