Wander, just wander
Venice is a magical city, and I would spend the first evening just strolling, getting lost, enjoying the city. San Marco by night is enchanting, and there is really no street or alley or area you need to avoid for safety sake. If I was going to spend just one full day, I think I'd skip Burano. Though it is a quaint little island, if you're looking for lace you can do better price-wise in Venice itself (just beware of the asian import imposters) and there are equally enchanting vistas in Venice proper. If I had just one day, I would hit up the Frari church (Santa Maria Gloriosa dei Frari), which is a big, hulking barn of a church, w/ stunning staturary and monuments inside. Take in the Doges Palace (spring for the "Secret Itinerary") if you have time, but the main thing to do in Venice for a day is just to wander. Stop in every church you see, cross every bridge you come to, slip down every alley. It's a small town, and you won't really ever get lost. Take lots of pictures, fill your water bottle w/ wine from the taps (sfuzi), and make note of all the places you want to go to the next time you're there, when you have more time, 'cause really, once you're there, you'll vow to go back. The most amazing thing about Venice is the quietness, the absolute absence of moter vehicles and bicycles makes for an amazing absence of sound.
Take a ride on the gondola.
You just have to take a ride on the gondola. No trip to Venice is complete without a gondola ride. The sights are beautiful, and the experience simply wonderful. A romantic 'journey' if you are with that someone special in your life.
Venice Clock Tower
Another Venetian landmark not to be missed is the Clock Tower.
Built over 500 years ago over an arch that leads to the old Merceria shops, it has an astronomical clock that has greeted all tourists and merchants to Venice for over half a millennium.
According to a story on the web,
"The clock shows the hours in Roman numerals, the phases of the moon and the Zodiac. It also gives indications to sailors about the tides and which months are more favorable for sailing. The Serenissima gave a large reward to the Ranieri brothers who constructed the clock tower, but legend has it that later their eyes were removed in order to keep them from repeating such a wonder."
The Doges palace and the Campanile
This is the view of the Marks Square you will get, whenever you arrive from the Lido.
The Doges palace and St.Marks Chatedral on the right and the Campanile ( the belltower on the left ) Make sure you go on top of the Campanile.
There is a lift going to the platform, where you will have a great view over the islands and the houses of Venice
As I mentioned earlier, try to...
As I mentioned earlier, try to make it during the festival. You will get an even greater appreciation, (and, indeed, passion) for the people that make up Venice, as well as meet some interesting people from all over the world. In this picture, I was just about to leave at the train station when an entire group of people dressed in crazy outfits like Robin Hood came out singing and handing out hard-boiled eggs. They were tasty! Too small to be chicken, but I didn't know enough Italian to ask! :-)