It can still be rainy in Belize in November, so it’s not an ideal time to visit. I quite like Belize and there is a lot to do there, including of course the second largest coral reef in the world. You can also head over the Guatemala border to visit Tikal and even down to Antigua for something different. You don’t get many great beaches there, but aside from that it is great.
Bali has nice weather in the first half of November and it’s very family friendly as long as you don’t stay on the nightlife streets of Kuta Beach. That is possibly your best choice. Dubai has great weather in November as well, and it’s very kid-friendly. There are shopping malls there that also have huge and modern play centers that are sort of like amusement parks there. And there are nice beaches as well. It’s unfortunate that the weather close to India limits your choices that time of year, but either of those could be great and they are both fairly affordable with frequent flights. Let me know if you have any other questions. -Roger
The three places that jump out to me are the Playa del Carmen area just south of Cancun in Mexico, the island of Puerto Rico, or Costa Rica. All of those have endless beach activities and sights and great food and everything else, and they are all well within your budget. Puerto Rico would be easiest, and probably my first choice. Costa Rica is better known for adventure activities that might suit the younger ones. There are several good resort areas along the Pacific coast that would work.
Unlike Bangkok, which has warm evenings and blazing hot days pretty much all year, Chiang Mai cools off nicely during December, at least in th evenings. This is an outdoor city with an emphasis on hiking and exploring temples so the cooler temperatures will be welcome for most people. It's still hot most days, and quite dry as well, so it balances nicely.
Sri Lanka doesn’t really have a good infrastructure for budget travelers at this point. There are loads of nice hotels if you are willing to pay US$40 or more per night, but almost nothing below that except for a few hostels. I haven’t been to Palawan but I have been to Boracay and Palawan can’t be too much cheaper. Boracay doesn’t have many budget options either, so my guess is that Thailand or Cambodia is your best bet.
If you’re a bit more on the timid side, you can always use Yelp and TripAdvisor to get good insights on places people have visited. As a disclaimer, some of the ratings may not be accurate on these sites, so make sure you go through and read some of the more recent reviews that people have written. We did this for a few of the places we visited and had no issues.