If you wanted to spend maybe 7 days outside of Singapore, I think I’d do 2 or 3 in Malaysia and then the rest in Thailand. Bangkok is another huge city but it’s also somewhat exotic compared to the other two, and much cheaper as well. Or if you wanted to spend some time on a beach you could instead go to one of Thailand’s islands. Phuket is the easiest to reach, but it’s not very interesting. Kho Phi Phi or Kho Samui are probably better choices because they really feel like islands (Phuket is more of a peninsula) and there is still plenty to do.
In India I’ve always had good luck with the trains by booking at least a couple days in advance, and also being flexible and only going when an AC3 ticket is available. As you know, the actual train stations are nightmares. But every hotel has a person who can fetch a ticket for you by going through the back door and bribing someone at the train office. Like a AC3 ticket might cost US$20, and for an extra US$4, your hotel will go buy it for you and it’ll be waiting at the front desk later that day. It’s a pretty sweet system.
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.