Interestingly, December though February do get a bit cool in Cairo, so it's not a great winter break, but in November it's still pleasantly warm and bone-dry so you can enjoy the outdoors for long periods of time. If you don't mind staying in a locally-owned hotel you can save a lot of money and see some old-world charm at the same time. Reservations in advance aren't necessary, but it's best to book your first couple of days just to avoid all the confusion once you arrive.
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.
The biggest single highlight in the region is the Angkor Wat temples near Siem Reap in Cambodia. It’s one of the most impressive tourist sights in the entire world, and Siem Reap is a fun and mellow town that you can linger in for a while. Vietnam is really lovely and cheap as well. The food there is excellent, as it’s a fusion of French and traditional Asian. You can go from Ho Chi Minh City in the south on the train to Hoi An near Da Nang, and then up to Hanoi to see Halong Bay. I wouldn’t start in Vietnam because it can be a bit trickier than the others. In the rest of the region it’s easy to book tours and buses and such, but in Vietnam the travel agencies are a bit harder to trust, so you have to be more careful. Things there are very cheap though, so even if you pay more for a reputable agency, it’ll still be cheap.
I think Sri Lanka would be wonderful for 2 weeks in December. The rainy season typically ends early in December, but even when it’s still going it tends to be quick downpours, as you are no doubt familiar with if you’ve been all over southeast Asia. Still at this point there are very few hostels with dorm beds and not even many cheap budget hotels, but at the age of 30 you are probably happier with normal hotels anyway. Value is quite good in Sri Lanka as long as you can spend at least US$30 or so per night, and hopefully a bit more. Food is also quite cheap in general, although there are still surprisingly few tourist-oriented restaurants in many towns so it feels a bit undiscovered. Just don’t spend much time in Colombo and preferably focus on the mountain areas, and I think you’ll love it.
If that doesn’t interest you I would point you towards the Playa del Carmen area, which is just south of Cancun and just across the strait from Cozumel. November is technically the last month of hurricane season and early in the month you’ll probably get at least a few quick rain storms, but actual hurricane in November are very rare. And at least Playa del Carmen is on the mainland and near a huge airport, so tourists would never be trapped there as they might on some small islands. Playa del Carmen is a fairly large touristy town with hundreds of little hotels, restaurants, bars, and things to do, so it’s good for a solo visit or with another person. Cancun proper, on the other hand, is mainly a long strip of beach hotels and time-share residences that are spread out and not well suited to solo visitors or small groups.
Trekking in Nepal during peak season might not sound like the most sensible choice for penny-pinching backpackers. But you can still enjoy the ideal weather without spending a fortune on in-demand hotels and expensive permits if you're happy to swap big-name trails, like Everest Base Camp and the Annapurna Circuit, for quieter treks to Kanchenjunga Base Camp and around the Langtang Valley. Idyllic conditions (dry but not witheringly hot) are also on offer in Rajasthan, one of India’s most vibrant and varied states. Chug between notable, attraction-rich cities like Jaipur, Jodhpur and Udaipur on an atmospheric and wallet-friendly Indian train, snacking on spicy pakoras and sipping sugary chai en route.