What is the least expensive transportation from the Venice airport to the Molino Stucky Hilton?
The least expensive option would be bus from airport to Piazzale Roma and then a vaporetto. Cost would be about 10 euro per person. Hotel's website provides some details on that option.
My wife and I had the pleasure of staying at the Hilton Molino Stucky when they opened last June 1. We were the first paying customers in their great Aromi restaurant. Of course, we were on our Hilton points.
There are a few ways to do this. First, you can take the very inexpensive bus ACTV or ATVO bus from the airport to the Piazzale Roma. The ACTV bus is really a city bus that I don't think has luggage racks. The ATVO bus is a bit more expensive (2E-3E more) but the bus has luggage racks. Then, you take the #41 vaporetto which goes counter-clockwise around the islands to the Palanca stop. Do not get off at the Sant' Eufemia stop. From the Palanca stop, you have a 1,500' walk to the hotel including crossing two foot bridges. The hotel does not have it's own vaporetto stop. You can also take the #2 vaporetto from the Piazzale Roma but make sure it's going in the correct direction.
Next, you can take the Alilaguna service from the airport to the Zattere stop (www.alilaguna.it). A bit more expensive and this service has limited stops on the islands. Fortunately, two of these stops are Zattere and San Zacceria. Zattere is across the Giudecca canal from the Palanca stop so you have to wait for a vaporetto going in the CORRECT direction to go one stop across the canal.
Almost finally, the hotel has two shuttles from the hotel dock to a private dock just to the east of the San Zaccaria vaporetto stop. They run in opposite directions every 30 minutes during most of the daylight hours. It runs less often in the evening. Oddly, they don't describe this on their website. Thus, you can take the Alilaguna to the San Zacceria stop and walk east a few hundred feet to pick up the free shuttle to the hotel. You'll see small Hilton sign at the private dock. They share the dock with another service.
Finally, you can take a water taxi from the airport to the hotel dock. This will cost you 100Euro ($155) for your party (including luggage). It's the most expensive option but the fastest by far. Feel free to message me if you have more questions.
You will absolutely love the hotel. As Hilton Diamond members, we stayed on the Executive floor. Everything was fabulous.