As a couple, Doge's Palace (Palazzo Ducale) works.
The grand staircases, the vast Tintoretto-ceilinged council chambers, and the chilling walk over the Bridge of Sighs into the old prisons give you the whole machinery of the Republic in one building. The honest catch: it's a long, dense, label-heavy visit that overwhelms unless you take the 'Secret Itineraries' tour or an audioguide to give it a story.