......As I, and many others, have posted many times, Venice is a place like no other, and while many locals have moved off the lagoon to the mainland (Mestre) due to high costs of living, the city largely thrives on tourism. In addition to the many fascinating areas - and Italian culinary delights - to enjoy here, many have found it worthwhile to also visit the nearby islands of Burano and Murano while staying in Venice.
However, I would suggest you might also want to venture onto the mainland and visit nearby, smaller villages like Treviso (below, left) Padua, Castelfranco, (below, right) and Cittadella, Bassano, to name only a few. Most of these are accessible via train, but renting an auto either at the Venice airport or Bus Park in Venice would afford more flexibility.
The university in Padua is where Galileo studied and taught and is the second oldest university (after Bologna) in the world. Unlike Castelfranco and Cittadella, which are walled cities, Padua also boast of the oldest coffee shop in Europe.
Cittadella, which means "little city", is quite famous for its medieval wall circling the city and dating back to the 12th century. You can actually walk along the catapult wall around the entire city, exiting at any one of four gates (like one shown at far bottom-left of photo.
Since I sell equipment for a company located here, I usually stay here and never get tired of visiting at any time of the year. While here, I normally take a side trip to either Castelfranco, or Bassano.
Bassano dell Grappa (above) is located in the foothills of the Mount Grappa (Italian Alps), and the home of Poli Grappa,
Other nearby towns of interest are Morostica and Oslo, and if you have enough time, Verona.
* One note of caution, if you do rent an auto at the Venice Bus Park, plan to return it to the airport, or you'll have to pay a hefty return fee - 40-60+ Euros!