Traveling in Italy

Define best. Cheapest? Fastest? How many people? How much luggage? Where in Castello?
There are at least 3 ways. Water taxi, Alilaguna public boat, and land bus plus vaporetto boat-bus. They all have their advantages depending on the situation.

Cheapest way to travel from airport to Castello, Calle Magno 2597, Castello, Venice, 30122, Italy.

The cheapest would be to take the No 5 bus from the airport to Piazzale Roma, then take the 4.1 boat to Celestia dock. Its is about 1/4 mile walk back to your apartment. There is a unified Aerobus+Ship ticket available for 14 EUR . If you are planning on getting a vaporetto pass during your stay, you can add the bus portion onto it for 6 EUR each way. Normally, the bus is 8 EUR by itself.
The bus portion will be about 30 minutes, the boat portion will be nearly an hour (Celestia is kind of a remote corner), and about 10 minutes walk. Use google maps to get the walking route.

The option with more walking would be the Alilaguna boat to Ospedale dock followed by a 1/2 mile walk. Cost 15 EUR. Boat takes 45 minutes from the airport, then 20 minute walk. You also need to walk about 10 minutes from the airport exit to the airport dock.

Sam is spot on about the cheapest way. We've done the No 5 bus from the airport to P. Roma and then the vap. to the area of our hotel many times. Piece of cake -- just as easy as can be. You can get a vap. pass with a bus ride (one way or return trip) added at the airport and avoid the crowds at the P. Roma vap. stop. Just be sure to scan your pass on the bus -- don't wait until you get to the vap. You can also order the vap. pass online and they'll send you a voucher you exchange for the pass at the airport. Not a bad idea since the credit card machines at the vap. office at the airport have been know to malfunction.