Unlike most cities on South America's west coast, Buenos Aires has fairly consistent rainfall all year long, and you might see a bit of the wet stuff even during December. Still, the temperatures should be ideal for being outdoors, and this is really mostly an indoor city anyway, so when it does rain you'll be able to pop into a shop or museum or cafe and have a great time.
In November you can find excellent resort deals all over the Dominican Republic, but Punta Cana is typically the first choice, especially if you are looking for an all-inclusive resort with all the luxury extras at a great price. The resort is actually a collection of little beach areas on the eastern tip of the island, so it's very secluded and well away from some of the confusion closer to the capital city.
If you are looking for first-rate destinations that are among the cheaper European cities, I’ll suggest Prague, Budapest, Krakow, and Berlin. You could visit all four of them by taking trains, or choose any one, two, or three. In December you can get quite a nice room in any of those cities, with Berlin being the most expensive by a bit. Food and attractions are also quite affordable in those cities.
The eleventh month of each year brings nice fall foliage, a nice pre-holiday calm, and tons of things to give thanks for—especially when it comes to traveling. From the Big Apple to the Sunshine State and all the way to the Pacific Coast, it’s easy to rest and relax before the seasonal hoopla by escaping into the grey blue skies and cooler temperatures of late fall by attending a star-studded annual parade, adventuring into the wonderful world of Disney with the kids, or even getting away to a tropical paradise to experience a warmer weather vacation getaway.
Southeast Asia is easier to deal with, and there are cheap flights connecting in the Middle East and landing in Bangkok, Kuala Lumpur, and Singapore. Each of those is a very interesting city, and there are many smaller places to go in the same region. In Malaysia there is Penang and Melaka. In Thailand there is Chiang Mai and quite a few others in that area. In Laos you can visit Luang Prabang, which sounds like it could be a winner for you. And there is also Siem Reap, which is home to the amazing Angkor Wat temple complex.