Free ATM in Venice airport?

YOUR bank is who is charging the fee. If your bank has an agreement with an Italian bank, you may not have to pay a fee. Just use any atm associated with a bank and decline the conversion to dollars.

In Italy a bank-owned machine is labeled a "bancomat", those operated by the post office are "postamat". If you see the word "ATM" then it's a private machine that usually is charging fees and giving a lousy exchange rate. In our experience it was hard to find a bancomat in airports, and tourist areas such as Sorrento tend to be loaded with ATM-labeled machines.

that usually is charging fees and giving a lousy exchange rate.

ATMs performing an ATM transactions do not have exchange rates, they simply dispense cash.

If you see anything about exchange rates or your home currency mentioned, you are not doing an ATM transaction, you are participating in currency exchange, or Direct Currency Conversion (DCC) Decline DCC, you can find more info on DCC by googling or searching on here.

You will run into DCC offers with any type of ATM (regardless of what you call them) as well as when using a credit card.

All of the ATMs at the airport will charge a fee for use, several euro, so if it is worth it to you, go ahead, or take your chances in Venice proper. However, since the Bancomats are a unified network used by most Italian banks. they will typically charge a fee of a few euro for Non-Italian bank cards.

According to a 1 month old YouTube video I recently checked out, there is a Postamat in the airport near the check in areas. Don't use any machine in Italy that calls itself an ATM. Use the bancomats or postamats.

Why not get some euros and bring them with you?
Your bank or AAA

Agree with the post above. Having Euros in hand when you land will eliminate a lot of hassle and stress. First you have to find a machine, usually wait in line to use it, hope it works (they do malfuncition at times and also run out of currency), and doing all that while jet lagged and on strange turf. The few extra dollars is will cost to get Euros from your bank or AAA is, in my opinion, well worth it -- and the extra cost is nothing compared to the overall cost of the trip. I'm not sure, but I think AAA has a "starter pack" that contains different denominations.

I've identified some bancomats and postamats near the rental. I will get Euro from one of these ATMs. Getting Euro at home takes time and is way more expensive. You bank will charge you a large fee, plus give you lousy exchange rate. If you are going to do that, you may as well use any ATM you encounter, because it will likely be easier and cheaper. You can easily find ATMs in Europe that are free or for a reasonable fee with a minimal amount of due diligence.

I don’t know where “home” is, but even here in the USA I always have cash and especially when traveling. Not uncommon in Italy to encounter paid toilets. Bring a small amount of Euros. In the big scheme of things a few Euros lost in the exchange rate is not a big deal. We have encountered machines that don’t work, won’t accept our cards, out of Euros, etc.