I’m in the Texas Hill Country myself at the moment (Kerrville to be exact), so we are almost neighbors. It really depends on whether you’d like a city or a beach or national parks and such. My first recommendation is Mexico City. You’ll be able to get cheap flights from Dallas, and the weather there in November is very nice and dry. Honestly, the whole huge city center is as nice as any large Texas city, and the architecture is far more interesting. You can even visit some pyramids just a bit outside of town. Before I went I assumed Mexico City would look run-down like many border towns, but it’s actually very fancy.
Another destination that might not exactly have “great” weather in December, yet deserves to be on the list, Sharm el-Sheikh is famously Egypt's most popular Red Sea beach resort. Those following the news might still hesitate to book a trip here, whether that is a rational decision or not. But at the very least this is one to consider in the future, as it's an amazing bargain once you get here.
The second trip will be the second week of December from the 13th to the 19th. Also warm place with adventure and tourism. Im going with my best friend. I was thinking one of the islands of the Caribbean or Latin America ( since I can travel freely to most of them without the process of getting a visa) but I’m not sure which ones where not affected by Irma.
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.