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LAST YEAR, I flew from New York to Berlin for a conference, but cleverly squeezed in an en-route day in Oslo, taking in the delightfully gloomy Edvard Munch paintings at a national art museum and savoring a leisurely lunch at an outdoor cafe. I not only sneaked in a side trip to a city I’d never visited, but shaved $500 off the price of flying nonstop.

Airlines often throw in a “free” stopover to encourage travelers to spend a few days in their home airports (the “free” simply means that the fare won’t rise if you…