Another option would be Cambodia and/or Vietnam. The town of Siem Reap, which is just next to the Angkor Wat Temples is the real highlight. Phnom Penh is worth a quick look, but not on a shorter trip. Vietnam itself is a wonderful and gorgeous country, and you can see a lot of the highlights in 10 days or so. It’s also very cheap, even around Christmas. You could fly into Hanoi and then go see Ha Long Bay, and then take a train down to Hoi An. After that you could go to Nha Trang for the best beach experience or the hilltown of Sapa. The city of Ho Chi Minh City is quite crowded and you might not like it for more than a day or two.
Traveling during the last ten days of December means crowds and exorbitant prices throughout much of the world, but the first two-thirds of the month—before holiday airfares and hotel rates go into effect—can be a serene, value-laden, and just plain lovely time to vacation. Europe is all decked out for the holidays—with locals generally friendly and in high spirits; in the Southern Hemisphere, spring is in bloom; and in the Caribbean, Hawaii, and Mexico, hurricane season is over, the weather is gorgeous, and there are free upgrades galore.

The rainy season is still finishing during November in Central America, but a bit north and south of that it's dry enough to make visiting very worthwhile. Better yet, it's still low season for hotels in most places even though the weather has gotten nice. Latin America is filled with excellent bargain choices and it has some of the best places to visit in November.
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. 
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