If I were you I’d fly into Bali and spend a couple days in the Kuta area to get your bearings and then head to Ubud, which is in the foothills and easily reached by shuttle bus. It’s also fairly crowded, but it’s still quite nice and there are scores of little spas and yoga places and that sort of thing. Then after a few days there, head up to the northern coastal town of Lovina, which is sort of like how Kuta was 25 years ago. It’s still only partly developed and there are still many open spaces, which is no longer true in the Kuta area. It’s cheaper than Kuta, and somewhat like Boracay in how mellow it is. You could also take a ferry from Bali to the island of Lombok, which is the next large one over. Things there are also more like Boracay and less chaotic than the Kuta area. Again, I really love Bali and still recommend it, but unless you are an Australian surfer, it’s best to stay somewhere other than the general Kuta area.
If you’re highly susceptible to the Christmas spirit and haven’t already committed the entire holiday season to wrapping presents with Aunt Linda, consider Cologne. The city has a whopping seven main Christmas markets -- definitely don’t miss the Cathedral Market, which has the largest Christmas tree in the Rhineland, or Angel’s Market, where you can sip eggnog punch and weave around people actually dressed as angels; Santa comes through once a week as well… on horseback. All that’s left for you to do is listen to the festive music and browse the stalls for an apology gift to send to Aunt Linda.
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.

Those countries are all very safe, and especially that time of year, you’ll be surrounded by dozens of other backpackers everywhere you go, including many solo ladies or girls in pairs. There is very little petty crime there, although it’s always wise to keep track of your belongings. It’ll be easy once you get there, and Bangkok is the perfect place to start. You can book a place near the famous “backpacker ghetto” of Khao San Road, which is quite affordable and really fun, as well as close to the top sights.
December is a popular month to go cruising around Hawaii and Mexico. It’s an ideal family trip, especially with most kids in the US out of school for the holidays. Experience the Hawaii’s tropical paradise. Pick a popular cruise liner and visit ports of call like Nawiliwili on Kauai, Honolulu on Oahu and Kona on the Big Island. If the Caribbean floats your boat, we recommend taking a cruise to explore Mexico’s Costa Maya, Cozumel, Ensenada, Acapulco, Cabo San Lucas, Puerto Vallarta and more. 

In SE Asia you have many choices, but probably the best choice for a family would be Phuket, Thailand. It’s more expensive than Goa, but the infrastructure there is much better. Patong Beach is the biggest town on the island and the main tourist hub, but for a family I’d recommend Karon Beach or Kata Beach, both of which are just a bit south of Patong, and both lovely.
Since flights to Mexico City from the US and Canada are usually quite cheap this time of year as well, this could be a perfect short cultural holiday. This city has great shopping, dining, and nightlife, and the central historic and tourist districts are far safer than most people would expect. There are ruins just out of town as well, so a bit of everything is available.
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