Copenhagen is regularly ranked among the world’s most livable cities. Certainly the international popularity of the Danish capital is well-deserved, thanks to its fine museums, grand architecture, great shopping and cutting-edge restaurant scene. However, few travelers discover the delights of Denmark beyond its largest metropolis. As I recently found on a 10-day trip through the countryside, this pretty, polite, peaceful country, roughly half the size of Maine, is a wonderful destination for delicious food, impressive castles and charming country house hotels. For many years, Falsled Kro, a longtime favorite on the island of Funen, was the only property I recommended outside Copenhagen, but now it’s been joined by several other addresses, which collectively form a splendid touring itinerary.