Vietnam and Sri Lanka could both be excellent choices for what you have in mind. Both are best for people who already have experience in these sorts of places, which you do. Twelve days could be a perfect length of time for a classic tour of Vietnam, flying into Hanoi and spending a few days there and in Halong Bay (with a possible side trip up to Sapa), and then taking the train down to Denang for a quick transfer to Hoi An. Hoi An is really a wonderful place and 3 or 4 days there would be great. There are good beaches nearby as well. Then take the train down to Ho Chi Minh City for a few more days before flying home from there. You could also do a side trip to Nha Trang (wonderful beaches) or Dalat up in the mountains. Vietnam really is gorgeous and the food is wonderful (French influences remain) but it can be a bit complicated for new travelers because you’ll find that many people you meet are trying to hustle you a bit, particularly travel agents booking trips and tours. The hotels are generally honest and great value, and so are the restaurants. You’ll learn to ignore the annoying people quickly.
The biggest single highlight in the region is the Angkor Wat temples near Siem Reap in Cambodia. It’s one of the most impressive tourist sights in the entire world, and Siem Reap is a fun and mellow town that you can linger in for a while. Vietnam is really lovely and cheap as well. The food there is excellent, as it’s a fusion of French and traditional Asian. You can go from Ho Chi Minh City in the south on the train to Hoi An near Da Nang, and then up to Hanoi to see Halong Bay. I wouldn’t start in Vietnam because it can be a bit trickier than the others. In the rest of the region it’s easy to book tours and buses and such, but in Vietnam the travel agencies are a bit harder to trust, so you have to be more careful. Things there are very cheap though, so even if you pay more for a reputable agency, it’ll still be cheap.
People don’t think of Moscow for winter, but it’s such a wonderful time to be there. The weather is no worse than what you’d find in New York City, and the huge advantage is the people—or, really, the lack of people! No masses of tourist buses descending on the Kremlin, no huge lines for museums (of course, we ensure our travelers skip all museum lines anyway), and no crazy crowds in Red Square. Something magical happens in Moscow in the off-season: It actually becomes more approachable and less intimidating. (Plus, December falls in the heart of the theater season, so for culture vultures this is the best time to visit.)
As with most on this list, hotels get very full and more expensive just before the Christmas holidays, so it's better to come early in the month if possible. That way you'll have your pick of places at some surprisingly good room rates, even at some high-end places on the famous beaches. If you are coming during Christmas then book a hotel NOW because they'll be full and will keep getting more expensive the longer you wait.

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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