Last resting place of Marco Polo
San Lorenzo (perhaps the most prominent of the city's churches closed for perpetual restoration) is also one of the oldest churches in Venice, founded in the 6th century, with a famous and wealthy convent established in 854 that later became notorious for the shenanigans of its frisky nuns.
An early version of the church burned in 1106, along with two dozen others, in a huge fire that convinced the Venetians that they should build with stone instead of wood. It was the last resting place of Marco Polo in 1324, only the great traveller’s body was misplaced or forgotten during its 16th-century restoration, so it's generally presumed he's still in there somewhere. The rebuilding was by Simone Sorella, best known for finishing San Giorgio Maggiore after Palladio's death. The French closed down the convent in 1818, and its famous relics (the mummified bodies of saints Leona Bemba, Giovanni, and Olinia and the torso of St Sebastian) were relocated to St Blaz in Vodnjan in Istria.
Currently San Lorenzo's convent is used as a retirement home, while the church itself was damaged in the First World War, deconsecrated, used as storage space, and remains currently 'under restoration'. Once in living memory (in 1984) it was called into service during the Biennale. As far as anyone knows that was the last time it was open; rumour has it that it's quite grand inside behind its unfinished corrugated facade—which may ring a bell among readers of Donna Leon's mysteries starring Commissario Guido Brunetti, whose office is nearby.
vaporetto San Zaccaria