It’s unfortunate and heartbreaking how many times I have recommended San Juan, Puerto Rico in the last few years. Once they get the power back on I’m sure it’ll be back to normal fairly soon after that, but I’m guessing probably March or later. And fortunately, Nate missed the Cancun area for the most part. Have you considered somewhere in the Cancun/Playa del Carmen/Cozumel area? I’m particularly fond of Playa del Carmen, and that flight to Cancun should be pretty reasonable for you.
Weirdly enough, Central America and South America aren’t really known as top “culture” destinations, as the colonial history has mostly wiped out the indigenous history in the larger places. There are Aztec, Maya, and Inca ruins and sights, but not really enough to build a whole trip around. I’d say the most interest of those would be the Inca culture of Peru, specifically around Machu Picchu and the valley around Cusco. Alternatively, visiting Argentina is pretty much like visiting Europe from a culture standpoint. It’s quite nice there and prices are low if you know about the blue market for currency, but otherwise it may not be what you are looking for.
The Maldives could be great if you can afford it. December is the most expensive month there, at least the second half of December. There are about 100 private-island resorts there, and most of them have water villas that start at around US$400 per night and go WAY up from there. But island rooms are cheaper. I wouldn’t recommend going to Male or any of the other populated islands that have several smaller hotels. It’s just not the same experience that you get from the private-island resorts. I can help much more with this if you decide to go to the Maldives.
Those countries are all very safe, and especially that time of year, you’ll be surrounded by dozens of other backpackers everywhere you go, including many solo ladies or girls in pairs. There is very little petty crime there, although it’s always wise to keep track of your belongings. It’ll be easy once you get there, and Bangkok is the perfect place to start. You can book a place near the famous “backpacker ghetto” of Khao San Road, which is quite affordable and really fun, as well as close to the top sights.
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.