There is so much history this is a great city to do a guided walking tour. Gondolas and water taxis are expensive, as is the food. There are an endless number of hidden passages, beautiful bridges and buildings, and stories. If you have time, a short boat tour around the city or to Lido Beach is also nice. The views from the water are incredible.
We've done many day trips to Venice when we were living in Austria. We aranged the itenerary based on whether or not our visitors/guests had been before and depending on the time of year (high season for tourism or not).
So, on one end of the spectrum, if you've never been you can start with St. Mark's plaza. Just getting there by water taxi will take you under the Realto Bridge and give you a good idea of the layout of the water canals and what life might be like living on a floating city. From there just walk around and enjoy shops, churches and cafes. Finding your way back walking will give you another view of life in Venice.
On the complete other end (from most tourist'y to less) you can skip Venice and take a water taxi out to the island of Murano and Burano. Murano is known for glass and Burano is known for lace. Such amazing, beautiful islands and brightly painted homes (on Burano) and businesses. There are far fewer tourists out there and you will get an idea of what Venice might have felt like before it got so famous.
You really can't go wrong. If you're an extrovert and have never been to Venice, head straight towards St. Mark's. If you're an introvert and prefer peace and quiet contemplation, do not go to St. Mark's. lol
Ditto on all of the good advice from the other replies. If you can, try to add an extra day and visit nearby Lake Como. Once, there, you can take a nice little boat ride to Bellagio and I think you would love it!
If it's at all possible I would stay overnight. The city has a much different feel without so many tourists late at night or in the morning. It's very inexpensive to book an entry time to basilica San Marco which is a great time saver!