Vietnam and Sri Lanka could both be excellent choices for what you have in mind. Both are best for people who already have experience in these sorts of places, which you do. Twelve days could be a perfect length of time for a classic tour of Vietnam, flying into Hanoi and spending a few days there and in Halong Bay (with a possible side trip up to Sapa), and then taking the train down to Denang for a quick transfer to Hoi An. Hoi An is really a wonderful place and 3 or 4 days there would be great. There are good beaches nearby as well. Then take the train down to Ho Chi Minh City for a few more days before flying home from there. You could also do a side trip to Nha Trang (wonderful beaches) or Dalat up in the mountains. Vietnam really is gorgeous and the food is wonderful (French influences remain) but it can be a bit complicated for new travelers because you’ll find that many people you meet are trying to hustle you a bit, particularly travel agents booking trips and tours. The hotels are generally honest and great value, and so are the restaurants. You’ll learn to ignore the annoying people quickly.
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.
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.