It’s no surprise that Thomas Mann set his masterpiece about doomed beauty, Death in Venice, in this city. The place has an air of decay about it, as though it is about to crumble into the sea. That persists even though 1,500 years have passed since the Venetians built their Serene Republic on a lagoon. These days, the city is more of a walk-through museum than a dynamic community. Its crisscrossing canals make it all-but impossible to grow, but its preserved quality, frozen in time, is unique and unmissable. It is hard to think of another city you can explore as thoroughly without motorized transportation. Still, its watery construction is becoming increasingly precarious with global warming, and Venice is steadily sinking. After years of alarm, the city is finally building a series of dykes. But local environmentalists fear that the budget-conscious project, launched during Italy’s deep recession, might work only for a few decades. For many tourists, the thinking goes, see Venice now before it’s too late. About 15 million people visit every year, and Venice can feel overrun by them. You won’t find any gondola rides on this list. But if you insist on taking one, there are hundreds of gondoliers who’ll gladly take you for a ride, figuratively and literally, for around $130. Instead, pack sturdy shoes, and walk. You can cover much of Venice in two days.