Many tourists only visit the main part of Venice that goes from the train station (or cruise boat port, or the parking lots) to St Mark’s square (Piazza San Marco), missing out on many neighborhoods (locally known as sestieri) and the other islands of the lagoon.
If you have the chance to, I highly suggest you make time to also go visit at least the islands of Murano, Burano and Torcello. The way to get there is to take the vaporetto, or waterbus; use the search feature for my “Transportation in Venice” blog post, where I explain how to move around.
Murano is known for the stunning work of the blown-glass artisans. The glass factories can be visited for free, so do not fall for the ones who charge money or for the first ones you’ll see out of the waterbus, wander around the little alleys and look for the free signs by the smaller factories/workshops. I do not advise doing this in the summer though, as it gets very hot inside the furnaces.
Burano is the island of handmade lace. This ancient tradition is still pursued in this beautiful place, with its houses painted in vivid colors and its slow pace, so different from the busy main areas of Venice and its tourists. Burano is also a fishermen’s island, therefore is a good spot for lunch if you enjoy seafood.
Torcello is close to Burano and is easily recognized for its leaning bell tower. It’s inhabited by only few families, very quiet and pleasant to visit.
There are other smaller islands in the lagoon, some scarcely inhabited, some in a state of abandonment and with ancient ruins, which cannot be visited unfortunately. For a listing you may refer to this page, which has the main ones: http://www.invenicetoday.com/islands/islands.htm. This website, done by locals, has some more good information on visiting the main islands: http://www.isoladiburano.it/en/.
Venice and its lagoon are included in the UNESCO World Heritage sites for its outstanding universal value. Read more about it here: http://whc.unesco.org/en/list/394.