In many ways November is the best month to visit Asia because most of the top destinations such as Bangkok and Hong Kong have excellent weather, but the big crowds don't start coming until just before Christmas. You can see on the list below that you have many excellent choices of destinations this month, and hotel prices are close to their yearly lows in many of them. In some cases it's better to visit in the second half of November because the beginning of the month can still be a bit rainy.
Those looking for beaches will be happy to see Phuket and Goa on the list, but there are many great cities that also have fine weather in November. You have so many great choices in southeast Asia that this is the perfect time to start a longer visit that spans several countries if you have the time.