We will arrive in Venice the day after Christmas (12/26) and will only have 1 additional day before our cruise leaves. Will anything be open?

Most likely, yes. Dec. 26 falls on a Friday, which is an important business day to remain open. Saturday is an important business day, too.

Thanks Wesley. I've read on this site that the day AFTER Christmas is also considered a holiday, so I wasn't sure.

Sorry, wesley, but I missed this thread and it deserves correcting. December 26, regardless of the day, is traditionally a second day off in Italy. Some businesses will open, especially in heavy tourist areas, but most will be closed. It's best to check ahead of time if there's something specific you want to see and do.

I wonder if they ended up eating at McDonalds'????

In Italy, both the 25th and 26 December are public holidays, so nearly all shops will be closed, but lots of cafés and restaurants will be open. Trains run a Sunday service, but rural bus services are limited. I once arrived in Venezia on Christmas Day and had no problem finding accommodation via the tourist office in the station, and had no problem finding places to eat and drink. Italians celebrate at home with their families on Christmas Eve but go out on the 25th and 26th.