If I had more information about destinations in East Africa that would qualify I would love to include them. But unfortunately, it’s one of the few regions I haven’t been to myself, and according to every source I hear, very few foreigners are visiting as well. I know many (especially wealthy) people do the safaris in that region, or they walk up Kilimanjaro, but outside that it still sounds like there is almost no tourist infrastructure or even a backpacker scene. If you know things to be different, please let me know because I’m very open to it. -Roger
In SE Asia you have many choices, but probably the best choice for a family would be Phuket, Thailand. It’s more expensive than Goa, but the infrastructure there is much better. Patong Beach is the biggest town on the island and the main tourist hub, but for a family I’d recommend Karon Beach or Kata Beach, both of which are just a bit south of Patong, and both lovely.

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. 
×