Staying There: Stella Maris, a whitewashed waterfront villa in Svendborg, is the island’s newest boutique property (from about $224; stellamaris.dk). For a lesson in Danish country chic, Falsled Kro, outside Faaborg, offers guest rooms and suites in thatched-roof cottages (from about $320 a night; www.falsledkro.dk). Broholm Slot, one of Funen’s most dramatic castle hotels, takes you back in time, with no televisions or telephones in the rooms (about $270 a night; broholm.dk).