Looking for Cheap Alternatives for Internet in Venice?
1) Bars and Restaurants – It may cost you the price of a beer (2€ + sit down fee), but if you see a sign for “internet” on their window display, ask if their wifi (pronounced wee-fee by some Venetians) works first, and pop in for a drink. Some places off the top of my head with Wifi are: the pizzeria called Birreria (in Campo San Polo #2168), some of the canal-side restaurants at the Rialto Bridge, and Hosteria alla Poppa (Santa Croce #1539, near Campo San Giacomo dell’Orio). There are many locales throughout the city, so just keep your eyes peeled.
2) The City’s Internet – While the city has launched a USD $14 million plan for tourists to access the Internet for €5 a day, don’t jump on that because the access areas are basically just along the Grand Canal, the main campos, and random parts of the city. For three days worth of web access in their “hot spots” around the city, the cost is 15€, so I would still go for option 3 (below) which gives you access all the time, and ALL over the country vs. just the city. However, if you still want to go this route, check out the Venice Connected site which has further instructions on pre-payment and such.
3) Rookie Pick: Italian Phone Carriers – Another option is check with your phone carrier to see if they have special international rates for Internet access (but this might cost your a fortune). If you prefer to go with an Italian phone carrier, make sure your smart phone is unlocked before you leave (call your provider and tell them you need to have the unlock code), so you can buy a new prepaid SIM (roughly €10 for a SIM just for data, or €25 for a “data + call” SIM card) through phone carriers like Vodafone, TIM, or Wind (all three stores can be found on either side of Rialto Bridge or in the Cannaregio district along Strada Nova-Ca’ d’Oro stop). With Vodafone, you can pay €3 a week to get 250MB of data transfer (in addition to the cost of the prepaid SIM card for smart phones). I actually prefer this option, because you will probably be in Italy visiting other cities and these prepaid plans work nationwide, so you’ll have phone access to make reservations, use text messaging, and have Internet and GPS capabilities (depending on your device). With €5 credit, you should be good for a week of phone and Internet usage all over the city (the internet costs €3/week and that leaves you with ten minutes worth of calling). You can buy €5 cards to top up if you need more credit. This can also work well for tablets.
Rookie Hint: Turn off DATA ROAMING on your cell or take out your American SIM card if you access Wi-Fi through your device, or you could incur serious roaming charges on your next bill.
Rookie Hint: You will need to bring your passport to buy a new Italian SIM card.
4) Hotel or B&B – B&Bs that do have Internet have them inside the rooms, while most hotels that claim to have Wi-Fi usually only have access in the lobby, so it doesn’t always work in your room.
5) Internet Cafes – Cost €7-9 per hour. I find that a bit much for logging on, but these places know you are probably desperate if you go to them. The good news is that they also usually have copy and fax services, which don’t come cheap, but at least it is a quick one-stop shop for these necessities. Most Internet cafés are open from 9am to 7pm, but a few stay open until 11pm Look for the “@” sign, which indicates the way to the closest Internet café. 
Rookie Hint: Remember to bring your passport, as Italy has an annoying login system which requires your personal information and proof of ID. Again, I say: go with the free wireless in the places mentioned above, or buy a prepaid Italian SIM.
Finally, you can always walk around the city in hopes of some unsecured WIFI, but that is iffy and most of those lines aren’t very stable.
ouch!! its so expensive!! i would better avoid to use the city’s internet