As for Malaysia, I’m a big fan, and with your friend there it should be easy. Interestingly, I was just in China myself recently and a few days ago I published a long article on my advice for whether to go yourself to China or go on a group tour. I also discuss the most popular and best places to visit when you are there in the bottom part of the article. One tricky thing for many of us is that you have to get a China travel visa and some of us can only get that visa issued in our home country, at least according to their rules. I literally spent years traveling around Asia but I was never able to visit China because they required that I get a visa issued in the US and I had to show my flights booked from the US to China and then from China back to the US. If I could have gotten a visa issued at a Chinese embassy in Bangkok or Singapore, I would have done it years ago.
Portugal does have one of Europe’s best autumn climates, but as you’ve noticed November can be a bit rainy. That said, in my experience it rarely rains for long periods in that part of Europe so I think it’s very unlikely that a big part of your trip would be “rained out.” Also those cities have lots of great indoor attractions so if you see that it’s supposed to be clear in the morning and drizzly in the afternoon, you can plan to explore neighborhoods in the morning and plan to visit a museum or castle in the afternoon. It’s a bit of a crap-shoot and generally Portugal has nicer weather than most of the rest of Europe at any given time. I hope this helps. -Roger
Aside from Indonesia you might also consider Thailand, which has great infrastructure so it’s much easier to travel with young children. Phuket has by far the most options, and its rainy season usually ends in early November. For families I recommend Kata Beach and Karon Beach, which are both just south of the main shopping and nightlife town of Patong Beach.
And if you are mostly interested in adventure and nature rather than cities, you might also consider India. The cities in India are complete insane asylums, but once you get outside of them it’s a beautiful country. The area of Kerala and its backwaters are a big highlight. They’ll remind you a bit of Sri Lanka in some ways, although things are cheaper and the scenery is quite different. The various beach areas of Goa, just to the north of Kerala, are also worth considering.
The high season hotel prices will start in November as well, but crowds are usually thin for most of the month so you should be able to get some nice bargains at some of the nicer places that allow online booking. When they see that they have lots of empty rooms as the month approaches, they'll discount to be on par with some of the 2-star places that aren't nearly as nice.
As for the hurricane, it’s true that it did go through that area a few days ago, but I think that was the first one in almost 10 years to do so. In other words, it’s an extremely rare event, and even when it does happen, they know about it long in advance so everyone is evacuated or safely sheltered. Also, the “Hurricane Season” technically goes through the end of November, but November hurricanes are actually far rarer than the earlier months. Personally, I love to book into places like Punta Cana during that season because the weather is the same about 95% of the day, and prices can be half as much as December or January.

If you are looking for an island that is moderately priced in late November I would probably head to Thailand. The rainy season typically ends in the middle of November in Phuket and Ko Samui and the other popular islands, although you might still get a few quick storms in late November. One nice thing is the crowds don’t start coming until mid December so you have a huge selection of hotels at really good prices.
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.