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
While December is quite busy in Lima, as a very popular summer beach destination for South Americans, it's also still very reasonably priced so it's worth considering if you are exploring the continent. The beaches aren't spectacular as they are in Brazil and elsewhere, but Lima is still a great summer city with great outdoor life this time of year.
From December through February there are literally no European cities that could qualify as having “great weather,” except for the Canary Islands, which is listed below. So during the winter Europe is all about cultural tourism, and lower hotel prices make it especially appealing for those who like to stretch their travel budgets and avoid crowds at the same time.
However, I would probably recommend staying closer to the US, unless you are really interested in the Asian cultures or that kind of experience. If you are mainly just interested in family time and a fairly easy holiday for all, and you aren’t specifically interested in getting to know an Asian culture and its food, I think I’d stay in the Americas.
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.
Overall this is a perfect time of year to visit almost anywhere in Argentina. When December arrives things really start filling up and all the locals are on their own holidays, so November is the ideal mix of great weather that isn't too steamy, and modest crowds and prices. With Argentina's recent inflation and currency devaluation, it can be hard to know how expensive this trip will be, but for most people it will be cheaper than in recent years.
Another tip is to look for apartments. If you’re visiting a large city, chances are they have plenty of new apartment buildings that are looking to rent out. Many of the larger hotel booking sites will offer you apartments for rent – and they’re very affordable. Not to mention, they’re much roomier and more than likely updated. You usually get a full kitchen, washing amenities (for laundry), a dinner table to sit and eat at, and a good sized bathroom that doesn’t make you feel cramped.
Resolve – My number one asset to staying on track was my resolve. I made my mind up before we left that I would not give in when tempted and that I would be entirely aloof for donuts, desserts, fries, and other favorite treats. I just kept reminding myself that I could enjoy those foods again perhaps on our next weekend getaway or at the end of our vacation if I chose to have a cheat day. Otherwise, they would be dead to me because I didn’t want my kids feeling guilty eating treats in front of me. I don’t want them ever to relate being good or bad based on what they ate so again; I had to have the mindset that it wasn’t a big deal.
You might also consider Malaysia and perhaps a stop in Singapore. Malaysia is actually more modern than Thailand so everything is easy and reliable. They have cheap VIP buses that are very comfortable. Penang in the north is really nice and also interesting. Kuala Lumpur is a modern and pleasant big city. A bit south of that is the colonial town of Malacca, which is also very nice and worth a look. Going south from there you can reach Singapore in a few hours, and that is an amazing city, although accommodation there is expensive.
In Rome, the Coliseum and Ancient Rome are outdoors, but the city also doesn’t get as cold as the others so most likely you’ll be fine if you bundle up a bit. In Venice, they often have those floods during December, but they come and go every 6 hours so even if you get unlucky you’ll still be able to get around half the day, and it’s a small city anyway.
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.