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.
Weirdly enough, Central America and South America aren’t really known as top “culture” destinations, as the colonial history has mostly wiped out the indigenous history in the larger places. There are Aztec, Maya, and Inca ruins and sights, but not really enough to build a whole trip around. I’d say the most interest of those would be the Inca culture of Peru, specifically around Machu Picchu and the valley around Cusco. Alternatively, visiting Argentina is pretty much like visiting Europe from a culture standpoint. It’s quite nice there and prices are low if you know about the blue market for currency, but otherwise it may not be what you are looking for.
New Zealand wines are world famous, and wine tours are popular with visitors. Auckland, New Zealand’s largest city, is set on the waterfront, with beaches, parks, and cruises to the nearby islands. The capital city of Wellington on the southern tip of North Island is home to New Zealand’s national museum, a great place to learn about the country’s cultural history. Christchurch and Queenstown are located on the South Island. There's so much to do in New Zealand — and it's convenient to reach on Air New Zealand’s nonstop flights from Los Angeles, San Francisco, Houston, and Honolulu, with a nonstop from Chicago to Auckland beginning Nov. 30.
Cambodia could work because Siem Reap is inland and the amazing Angkor Wat temples are worth a full day or two, and the town of Siem Reap itself is quite nice. You could actually combine a couple days in Siem Reap with a few days in Bangkok, and take a (cheap) luxury bus between the two. Bangkok is a really fascinating city with a lot to see, plus it’s a great transport hub. The other main non-beach option in Thailand is the city of Chiang Mai, which is wonderfully inexpensive with quite a bit to see. It’s even a bit cool during December, so that might be a nice change of pace from India. Many people are also going to Myanmar these days, although I haven’t been yet so it’s hard for me to recommend it. I’d say if you combined 2 or even 3 of these places you could have a very interesting holiday.
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.