The first thing to know about this gleaming white palace on the shores of the Alster, built for transatlantic passengers in the early 1900s, is that it’s one of the world’s truly legendary hotels. The second is that with a little internet sleuthing you can book one of the commodious, high-ceilinged guest rooms, not too many of which are alike, for not much more than what you’d pay for a business-oriented hotel in Hamburg. Of course, many of the guests could care less about costs: Madonna, Mick Jagger, Elton John, and a long roster of other notables stay here when in town, as do savvy travelers who feel at home in the surprisingly cozy lounges, sophisticated art deco bar, and guest rooms well stuffed with comfy arm chairs and plump bedding. No doubt they all enjoy the sweeping staircases, lake views, indoor pool, meticulous service, and atmosphere that is a lot more laid back than you’d expect from such regal surroundings.