Actually, all of my best suggestions for those things are in the article above. One challenge you’ll have is that all popular tropical destinations have their peak weeks at the end of December because so many people in cold areas have that time off. So flights to Central or South America are going to be fairly expensive, although buying soon can help. For hiking and views I think Costa Rica could be a good choice, or Nicaragua. You could also go to Bariloche in Argentina, though it’s probably not worth going all that way unless you were also going to spend some time in Buenos Aires and such.
In spite of its image of being blazing hot all the time, December in Cairo can actually be on the cool side, at least in the evenings. This is great though because almost all the important sights are outdoors and requite a lot of walking between them. For 9 months of the year it can get very hot doing that, so these few cooler months are ideal for visiting the famous sights.
The reason for the recommendation is that Bali is not only a yoga and “spiritual” hot spot, but it’s also the most popular island for solo women travelers in the region. The book and movie “Eat, Pray, Love” was inspired by this trend, and they have in turn inspired thousands of solo female visitors to go there and stay for long periods, particularly in and around the Ubud area. It’s gorgeous and quite cheap once you get there, and the locals are generally gentle and kind to all. Most other tropical hot spots in Asia have far more solo male visitors than solo females. Just avoid lingering in the Kuta Beach area, because it’s packed with bars and loud backpacker party people. Most of the rest of the island is quite mellow.
With a vibrant downtown, great restaurants, culture, and a recent multi-million renovation to the Ritz Carlton, Naples, one of the areas most luxurious hotels, December is when the town really starts to get into gear. You can spend your time on the miles of gorgeous Gulf Coast white sand beaches, take an Everglades Safari, or head to the Artis-Naples which hosts world class dance, theatre, music, and comedy. And that is to say nothing of the five-star shopping.
Dubai has pretty much perfect weather in November, and this is really the first month since April when it's not scorching here. Fortunately, the crowds are also light because most people wait until Christmas to start traveling to warmer places. Dubai can be incredibly expensive if you have a big budget, but it doesn't have to be. You can get good deals on non-chain hotels and even apartment hotels this month, and if you skip the hotel restaurants and the fancier places in malls, you can eat well on a modest budget here.
On my own trip I spent 3 nights on the North Island after leaving Auckland, and then 4 nights on the South Island. The South Island is more scenic and interesting, and much less crowded, so I would have liked to have stayed another 2 or 3 nights if I had the time. So I’d recommend 3 or 4 nights on the North Island and 5 to 7 nights on the South Island. With smaller towns and smaller crowds on the South Island, that is the better place for star gazing, though most of the North Island is fairly empty as well. It’s an amazing place and I’m sure you’ll love it. Have a great trip. -Roger
Pretty much everywhere is going to be at or near capacity for those dates because half the world is on Christmas break. Between Australia and New Zealand, I think New Zealand would be far more interesting for 10 to 14 days. In Australia you pretty much have to spend a few days in Sydney, a few days in Melbourne, and a few days at the Great Barrier Reef, all of which require flights and will be very crowded over those weeks.
Oh, did you want a sunny tropical vacation that doesn’t require a passport? Done. Hurricane season is over, flights are cheap, and the water is still warm enough for swimming (and scuba diving). Almost all the tourists come here via cruise ship, which means you’re mostly not competing with them for hotel rooms -- Windward Passage, Emerald Beach, and the Bolongo are all open for business after Hurricanes Irma and Maria last year. On December 16 you can catch Jazz By The Sea down at Coral World Ocean Park, and on December 21 watch the St. Thomas Lighted Boat Parade, where contestants (boats) are judged on lights, originality, and holiday cheer.
Mauritius would be an interesting option if you wanted to mainly stay in one place, which I think is typical on a honeymoon. Sri Lanka is fascinating and really nice, though most people who visit tend to tour around seeing some beach areas and some of the hills and jungles. So I’m not sure if it’s ideal if you want to just stay in one place. Kerala has some really nice resorts that are within easy reach of the backwater boat tours and other attractions.
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.