Fortunately, it rarely rains at all in Cairo, so even though December is one of the wetter months, that means nothing and you are unlikely to see even a drop of rain. Hotel prices do reach their peak in Cairo starting late in December, so it's best to go early in the month if possible. Egypt is definitely one of the cheapest places to travel in December, and the weather is surprisingly nice as well.
I totally agree about the solo traveling thing being down to luck in many cases. Right now I’m on a long trip around Europe again, and from one night to the next I might meet a bunch of interesting people, or be sitting there alone in a sea of locals with no interest in chatting with foreigners. At least in a place like Goa, everybody is on holiday, so I’ve had good luck meeting people.
My top recommendation would be San Juan, Puerto Rico. It offers a wonderful mix of history and culture and nightlife and great food, alongside excellent beaches and abundant activities. Hotels and rental apartments are mostly in the mid-range for the Caribbean, but food and drinks and most other things are great value. You could get a place in the Condado area, which is close to the lovely Old San Juan neighborhood and plenty of nightlife all around. And then perhaps you could rent a car and stay for a few days at one of the smaller beach towns elsewhere on the island. You wouldn’t even need a passport, although it does feel fairly exotic while you are there. But because it’s part of the US, it’s also well organized and safe. Most people you’ll meet will speak at least some English, and many are fluent, so it’s easy even if you don’t speak Spanish.
That’s an interesting question. On my main list of Caribbean destinations ranked from cheapest to most expensive, I have a list of the 6 islands that suffered heavy damage and are not going to be open for normal business this coming winter. But that leaves 26 other destinations on the list where things are totally normal. Fortunately for the industry in general, the busiest destinations such as Jamaica, Dominican Republic, and the Cancun area, are all still unscathed.
This is a really interesting question. If you want to avoid crowds then you have already figured out that it’s best to avoid Honolulu and I would avoid Oahu completely. The Big Island is very interesting because of the volcano and some of the other scenery, but the most beautiful islands are Maui and Kauai. I haven’t made it to Kauai yet, but everyone I know has been there and they swear it’s the most photogenic, which looks right based on the photos I’ve seen. Maui is also really gorgeous and all islands other than Oahu are uncrowded even in high season. I drove all over Maui in a rental car and loved it and I don’t think there is as much to see on Kauai. So either of those will be great choices and the weather should be almost perfect in December with warm (but not scorching) temperatures and almost no rain. Have a great trip and let me know if you have any other questions. -Roger