For the record, the official Hurricane Season runs from June 1 to November 30, but hurricanes in November are extremely rare, so we have likely seen the last of them for this season. The devastated islands will need help rebuilding, and the remaining islands are hoping that visitors know they need the business as well, and that there is no risk of big storms starting in December and usually earlier. -Roger
The hotel rates all over Goa are highest in December and January, but in Anjuna or Vagator they still start at around £10 per night for a private room with ensuite. The cheap places are quite shabby, so it might be worth spending more. Vagator has an amazing beach, but it’s often filled with Russians these days. Anjuna is famous for its beach raves and music scene, but I’ve honestly heard nice things about many other beach areas in Goa.
The last suggestion would be to start in Bangkok, which is an amazing city even if you avoid the Khosan Road party area, and then head south along the coast and into Malaysia and finally Singapore if you feel like it. There are many nice beaches and islands in Thailand that aren’t filled with party folks, and some really interesting places in Malaysia as well. George Town on Penang is really nice with excellent food, and Kuala Lumpur is my favorite city in Asia for few reasons. The town of Malacca is really nice, and Singapore is amazing, if a bit expensive.