Get off the beaten track and explore the smaller canals. Walking along the main canals, you will find it packed with tourists. Make a slight detour and you will find yourself all alone to wander the canals with your beloved.
Eat in an authentic Italian trattoria. Soak up the sounds, sights and smells of Italy and watch the people go by. Have a glass of Italian wine and congratulate yourself of having the great idea to visit Italy.
Find an out of the way bridge over a canal to watch the sunset. Have a gelati and enjoy the scenery.
Quick Tips:
Unless you have your heart set on it, give the gondola ride a miss. For for a 45 minute ride, it's extremely expensive.
You can watch the gondolas drift down the canals for free. You might even catch one serenading someone, which is nice and won't cost you a cent.
No one that I have ever spoken to has totally raved about it so I would save your money for a romantic dinner out.
Do get a good map right away. Venice is an extremely confusing city to navigate and you will definatly need a map.
Best Way To Get Around:
The best way, without a doubt, to enjoy Venice is on foot. Cars are not permitted in Venice (only on the outskirts) so you will not be able to drive.
You can take the vaporetto if you get tired of walking. A vaporetto is a water ferry that transports people from stop to stop. Tickets cost 6,000 lire per trip. It is possible to get a 10 ticket book for 50,000 lire if you feel you will be using it alot.
Personally, I feel a lot safer on foot. The amount of people they cram on those buckets of bolts is enough to make me a little nervous!
Water taxis (speedboats) are also available but are very expensive.