1. Do try the Italian gelato ice-cream. It's very popular, worth the money, and a speciality here.
2. The shops at the Square are very pricey. You can easily get better prices, a small distance away from the Square.
3. If you're here for a longer period of time, you can even check out the various cruises that start from here and the variety of packages available.
4. Gondola ride here is a must. It's a 40 minute ride in a gondola (boat), and takes you deeper into the canals of Venice. Without such a ride, it's difficult to truly experience the city. A gondola can seat 6 people at a time, and costs 80 euros per boat, however, bargaining is the norm.