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.
Since flights to Mexico City from the US and Canada are usually quite cheap this time of year as well, this could be a perfect short cultural holiday. This city has great shopping, dining, and nightlife, and the central historic and tourist districts are far safer than most people would expect. There are ruins just out of town as well, so a bit of everything is available.
As a male who usually travels solo, I’m not sure I’m the best source of advice for solo female tips. There are hundreds of travel blogs run by solo female travelers, and if you Google some specific topics that you are curious about, I’m sure you’ll find some great information. Generally speaking, the females tend to say that traveling solo is far easier and less threatening than they had feared.
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.
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