If you are interested in a place that isn’t focused on beaches in that area then I’ll point you to some recent answers just above where I mention the charms of Chiang Mai in northern Thailand, or Luang Prabang in Laos, and/or Siem Reap in Cambodia. All of those are wonderful places with temples and other sights, and they are quite affordable once you are there as well.
As you suspected, this is a tricky one. Most of the places that would work for you are having a very rainy month in November, so it’s not a good time. Thailand would actually be a good choice if you can deal with the travel time. The rainy season there ends in October and yet the crowds don’t start appearing until December, so you get low hotel prices with nearly perfect weather. As mentioned, all of the good options in Central or South America have a wet season in November. Argentina could be a good option, as November is late spring there, and it has everything you are looking for. The flights to get there are also fairly long though.
Make like a Viking and soak those sore muscles in one of the many outdoor heated pools, some hidden away and others modern day gathering spots. The famed Blue Lagoon is Iceland’s best-known geothermal spa with temperatures of 98-104 degrees Fahrenheit. The lagoon’s waters are rich in minerals like silica and sulfur and are reputed to have healing powers for skin problems. There are saunas, lockers, showers, and towels available for a reasonable fee as well as restaurants and a lagoon side bar. Whale watching, though not prime season, is always an option in Iceland, as is dog sledding — on snow if available or dry land if not. Either way it is an amazing experience, and the meet and greet part allows you get up close to these beautiful dogs.  The younger crowd might enjoy the Iceland Airwaves Music Festival to be held in Reykjavik this Nov. 7-10 showcasing hundreds of acts, both famous and newcomers. Venues include bars, bookshops, theaters and concert halls.
Thank you for the kind words. I know what you mean about the image of Thailand and Bali, particularly among Australians. On one hand you could go to either of those places and easily avoid the most notorious party neighborhoods, but it’s probably easier to head somewhere else since both of those places are so crowded that time of year anyway. I do have a few suggestions, which I’ll describe briefly and then if you want more details about any that appeal to you I can do that in a follow up comment.
This is a huge question and I’d need to know more about your preferences and your budget to answer it properly. But I can give you a short version here. In my opinion, which is matched by many other people, the most interesting and dramatic cities in Europe are London, Paris, Amsterdam, Rome, and Venice. Visiting those would require about 16 days to do it properly because you’d want to spend 3 or 4 days in each city, except maybe only 2 days in Venice because it’s quite small.
Islands full of olive groves, sparkling Adriatic beaches, and romantic medieval cities begging to be explored; Croatia is an idyllic European escape. If you’ve dreamed of wandering the walls of the ‘Pearl of the Adriatic’, Dubrovnik, without all the tourists and hordes of Game of Thrones fans, November is your month. The weather is still warm, the water bath-like, and the families and backpackers have dispersed – which means you can beach in peace. Or why not try one of our sailing adventures, and island-hop your way around the stunning coastlines on your own private yacht?
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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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