That is an interesting request. I’ve spent about 18 total months in those countries you mention and I’ve yet to see a single rat. If your fear of rats is just that, you could go to any of them. But if you have a more general fear of things that are untidy then I’d definitely avoid India. It’s a fascinating country, but there are piles of garbage all over the place.
The three places that jump out to me are the Playa del Carmen area just south of Cancun in Mexico, the island of Puerto Rico, or Costa Rica. All of those have endless beach activities and sights and great food and everything else, and they are all well within your budget. Puerto Rico would be easiest, and probably my first choice. Costa Rica is better known for adventure activities that might suit the younger ones. There are several good resort areas along the Pacific coast that would work.

The Maldives could be great if you can afford it. December is the most expensive month there, at least the second half of December. There are about 100 private-island resorts there, and most of them have water villas that start at around US$400 per night and go WAY up from there. But island rooms are cheaper. I wouldn’t recommend going to Male or any of the other populated islands that have several smaller hotels. It’s just not the same experience that you get from the private-island resorts. I can help much more with this if you decide to go to the Maldives.
Those wanting to hike to Machu Picchu will also find this to be an ideal month, since getting in a group will be easy even without much advance notice. The train to Machu Picchu is expensive year round, and reservations should be easier to get the day before this time of the year. Hotels are always cheap in Cusco so you can afford to get something nicer than you are used to this month.

Bali, which is just south of the equator, would be a good choice in November. It does rain a bit that month, but they are summer storms that tend to only last 30 minutes or so. It’s a wonderful island with great prices on most things, including massages. The complicated thing about Bali is that the main tourist areas of Kuta, Legian, and Seminyak are now so crowded that they can be unpleasant. I spent a month there again earlier this year, and I don’t think I’ll go back to that part of the island.
On the hunt for a non-traditional ski vacation? Look no further than the Japanese Alps. According to American Express Travel, the region has seen an increase in bookings during the holidays in recent years. And while December has historically been less popular than Japan’s peak season—April-November—adventurous travelers are now intrigued by the wilderness of Japan in the winter. The Hida, Kiso, and Akaishi alps are home to indigenous snow monkeys, volcanoes, and lava plateaus, plus, visitors are drawn to the area for its pristine ski offerings, natural hot springs, and rural hiking.
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.
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