Further south still is Dorsoduro, one of the city's most arty districts (boasting both the Peggy Guggenheim collection and the world famous Accademia) with its wide Zattere promenade looking across to the island of Giudecca.
If you have more time, there's life outside central Venice, too, on the islands of the lagoon.
Relax and star-spot on the glamorous beachfronts of Lido, pick up some exquisite hand-blown glass on Murano or antique lace on brightly painted Burano before unwinding in the medieval Santa Maria dell'Assunta cathedral on Torcello.
Or follow the example of the Venetians and escape to some of the 30 or so smaller islets dotted around the lagoon.