Like so many others on this list, Goa is completely done with its harsh rainy season by the time November begins, yet crowds don't really start showing up in earnest until mid December. If you have the time off then you'd be very happy just finding a cheap hotel in one of Goa's beach towns and just chilling the whole month in great weather and with minimal crowds.
Oh, and I just noticed you asked about general safety as well. Buenos Aires is fine as long as you don’t wander into the bad neighborhoods after dark, which is pretty much true almost anywhere you go, including Europe. But Rio is sadly famous for petty crime and it’s a real issue. As long as you know what NOT to do it’s quite safe, so I’ll still recommend it as long as you read up a bit on the topic. The most common problem is when people walk down to the water on the beach after dark. As long as you know NOT to do that you should be fine, but if you did go for an evening walk near the water and out of sight of the well-lit sidewalks, the chances of getting mugged are extremely high. Again, it’s worth learning about it and it’s easy to stay safe if you do. Let me know if you have any other questions. -Roger

That was very nice of you to take the time to mention this. Interestingly, I’ve been to Bali exactly twice so far (going again in early 2016) and both times have been in December. As you have probably noticed, the rainy season in Bali can be VERY rainy at times, which is why I didn’t put it on the list during the worst months. I still clearly remember standing in almost 2 feet of water trying to push the minibus I was riding in to a dry enough area to start the engine again. That was on the way to Ubud, but most of the time the rain isn’t problematic and I’d go back again again in December if given the chance. Just don’t expect any Christmas decorations or celebrations because they pretty much ignore it there, even in tourist areas. Have a great trip. -Roger
It's getting cold out there, so consider a journey that leads you into a warm museum. Whatever your interest, there's bound to be a specialized one to engage it. If art and sculpture are your passions, discover some favorite art museums around the world. And consider that you can make a day of it soaking up culture as many contain surprisingly good restaurants to visit in between your viewing.
Make like a Viking and soak those sore muscles in one of the many outdoor heated pools, some hidden away and others modern day gathering spots. The famed Blue Lagoon is Iceland’s best-known geothermal spa with temperatures of 98-104 degrees Fahrenheit. The lagoon’s waters are rich in minerals like silica and sulfur and are reputed to have healing powers for skin problems. There are saunas, lockers, showers, and towels available for a reasonable fee as well as restaurants and a lagoon side bar. Whale watching, though not prime season, is always an option in Iceland, as is dog sledding — on snow if available or dry land if not. Either way it is an amazing experience, and the meet and greet part allows you get up close to these beautiful dogs.  The younger crowd might enjoy the Iceland Airwaves Music Festival to be held in Reykjavik this Nov. 7-10 showcasing hundreds of acts, both famous and newcomers. Venues include bars, bookshops, theaters and concert halls.
Hmmm…this is a tricky one. Since you want to get out of SEA, you might have to go a long way to reach someplace that could be considered cheap and also has decent weather in December. Japan and South Korea will be cold, and not really cheap. If you go south you hit Australia, which is very expensive by most SEA standards (although not bad by Singapore standards). Perth is obviously closest and it’s a real city, and of course Sydney and Melbourne will be in early summer in December so those could work if your budget allows. Brisbane and Cairns are both known for outdoor activities, although nightlife might be tough for teenagers and there are no real cultural sights.
This is a huge question and I’d need to know more about your preferences and your budget to answer it properly. But I can give you a short version here. In my opinion, which is matched by many other people, the most interesting and dramatic cities in Europe are London, Paris, Amsterdam, Rome, and Venice. Visiting those would require about 16 days to do it properly because you’d want to spend 3 or 4 days in each city, except maybe only 2 days in Venice because it’s quite small.
Mauritius would be an interesting option if you wanted to mainly stay in one place, which I think is typical on a honeymoon. Sri Lanka is fascinating and really nice, though most people who visit tend to tour around seeing some beach areas and some of the hills and jungles. So I’m not sure if it’s ideal if you want to just stay in one place. Kerala has some really nice resorts that are within easy reach of the backwater boat tours and other attractions.
But if you wanted more to explore the area near Singapore then Malaysia and Thailand are the obvious choices. The three most popular stops in Malaysia are Malacca, Kuala Lumpur, and George Town on the island of Penang. I quite like all of those so it’s hard to recommend one over another. I really like Kuala Lumpur and have spent quite a bit of time there, but honestly compared to Singapore it seems a bit untidy and old fashioned. In other words, if you are tired of a big and busy city like Singapore, then don’t plan much time in KL. Malacca and George Town are both smaller tourist cities with great food and interesting sights. There is frequent and cheap bus service from Singapore going through Malacca and onto KL. Then more buses from there to Penang and onto Bangkok.
Surprising to some people, December can actually be a bit cool in Mexico City, especially at night. Its elevation keeps it mild all year, but at least the rainy season is totally over by December, so it's an ideal month for a cheap cultural holiday, perhaps combined with a trip to one of Mexico's many beach resorts. You can get cheap flights between Mexico City and Cancun or Puerto Vallarta, for example.

Hotels in Buenos Aires are starting to reach their summer peak prices in November, especially toward the end of the month, but still they are a fantastic bargain by European or North American standards. The weather in November is also pretty much perfect, and while there's always a threat of rain in BA, it's mostly an indoor city so it shouldn't be too much of an inconvenience.

November brings the annual Vodafone Mexefest Music Festival (Nov. 24-25), a gathering of popular artists in venues throughout Lisbon. The Lisbon & Sintra Film Festival, in its 12th year, is a celebration of cinema with directors, actors, artists, musicians, and writers in town for the event (Nov. 16-25). Billed as the “largest technology conference in the world,” Web Summit began in 2010 as a way to connect industry and the technology community (Nov. 5-8). The year’s new wine and the ripening of chestnuts are celebrated with the Magusto, on Nov. 11, St. Martin’s Day. The holiday spirit becomes apparent at the end of the month, with colorful lights and roasted chestnut vendors along the streets.
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