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.
The best places in December with good weather and that are inexpensive and also fairly close to India are Sri Lanka and Thailand, and they are both mentioned in the article above. Sri Lanka is obviously closer and you have many nice and scenic areas in the hills as well as the beach areas along the southern coast. But Sri Lanka has many similarities to India, as you may know.
It would help to know your starting location, but I’ll assume it’s the US or Canada because you didn’t say. My first thought for this is Argentina, which of course is in mid spring in late October. Buenos Aires is a wonderful city with great food and culture. You could also visit Mendoza, which is the lovely wine region, and Bariloche, which is a mountain resort area with year-round activities and such. Then there is always the amazing Iguazu Falls on the border with Brazil and Paraguay. It’s by far the most amazing waterfalls and area I’ve seen. Things are pretty cheap in Argentina these days for outsiders because of their weak currency. It’s also got very good outdoor activities in many different areas that should have nice weather in late October. It’s easier if you know Spanish, but still doable if you don’t. I don’t speak Spanish and I enjoyed it so much I stayed for a month. Let me know if you have something else in mind and I can try again. -Roger
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.