The high season hotel prices will start in November as well, but crowds are usually thin for most of the month so you should be able to get some nice bargains at some of the nicer places that allow online booking. When they see that they have lots of empty rooms as the month approaches, they'll discount to be on par with some of the 2-star places that aren't nearly as nice.
Actually, most of the popular European cities have fairly mild winters, in that they don’t spend much time below freezing and snowstorms are rare as well. It’s hard to make suggestions without knowing about your tastes, but I will tell you that the most popular European cities are London, Paris, and Rome, and none of them get snowed in often. If you are going to Italy, you should also go to Florence and maybe Venice as well.
November is a wonderful time to explore this diverse country without the crowds and heat of the summer months. The ancient city of Marrakesh presents an uncommon blend of ancient traditions and modern conveniences. Accommodations include traditional Moroccan houses, or riads, once the homes of upper class Moroccan families. Riads range from budget-friendly room rentals to luxurious palace-like dwellings. Shop the souks or markets of the old city for leather goods, textiles, pottery, spices, and much more. Be prepared to haggle with the vendors for the best prices.
In November you can find excellent resort deals all over the Dominican Republic, but Punta Cana is typically the first choice, especially if you are looking for an all-inclusive resort with all the luxury extras at a great price. The resort is actually a collection of little beach areas on the eastern tip of the island, so it's very secluded and well away from some of the confusion closer to the capital city.
Spend the past two days discussing your ideas. Group thoughts; Is that adventurous and cultural enough? We want a “wow” factor. We have vacationed in Cayman Islands about a dozen weeks since the kids were little (been there done that.). We have ruled out Asia only because don’t see a huge Wow factor for the amount of travel. What about African Safari? Still not ruling out your ideas, just want to know what is Wow about Puerto Rico? Costa Rica?
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Since you mention the temperature in Fahrenheit, I’ll assume you are in the United States. You might have to go to the Southern Hemisphere to reliably get 84F or higher, but you can get over 80F in most of the Caribbean. You’ll get low 80s in Hawaii in early December as well. Fortunately, neither of those places get too crowded until just before Christmas, so either should work.
Of the others, I’d say that Thailand would probably be your better choice. Goa is obviously famous for its beach parties, and drugs are easily available there just in case that is important, but there really isn’t much else to see or do there. Goa is a collection of beach towns, some of which are filled with raucous Westerners all winter. But once you go inland, it’s kind of falling apart, and it’s not even very “Indian” because it was run by the Portuguese until about 60 years ago.
In Vietnam every hotel will have a “tours desk” that will happily book a tour or visit to any local sight imaginable. There are also dozens of independent travel agencies around booking these same tours, but some of them are better than others. I prefer to book tours through my hotel, even if it costs a bit more, because it helps them and they have a strong incentive for you to be happy with the tour. If a hotel would consistently book guests on tours that the guests felt were rip-offs, that would be in the reviews and they would lose future business. More expensive hotels tend to charge more for the same tours, but things in Vietnam are so cheap that it’s not worth worrying about. And you might get a better pick-up at the nicer hotels as well.
Even though November is one of the busy months in Pokhara, they've built so many new hotels in the past few years that finding a room – even at a decent price – should always be possible. The high-season rates are still very cheap by almost anyone else's standards, and food and drinks are always very affordable, but if you look around a bit you'll be able to do even better.
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.
If this were last year I might have also suggested San Juan, Puerto Rico or Cartagena, but both of those have issues at the moment. If for some reason you don’t like what you see in Costa Rica, there are also some really nice resorts in Panama, especially in the San Blas Islands area. Aside from those you’d probably have to fly longer than you prefer. I hope this helps. -Roger