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.
While December is quite busy in Lima, as a very popular summer beach destination for South Americans, it's also still very reasonably priced so it's worth considering if you are exploring the continent. The beaches aren't spectacular as they are in Brazil and elsewhere, but Lima is still a great summer city with great outdoor life this time of year.
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.