Any public swimming pools near Venice, Florence, or Rome?

In Venice go the beach the Lido!!

regarding mens swimming attire.. I bet it is the same in Italy as France.. boardshorts that are commonly worn as swim suits in North American etc.. are not considered hygenic as as a swim suit , because they can be worn as street wear.

In Florence we stayed at a lovely Agritourismo( just outside Florence) that had a nice outdoor pool.. I bet that would be hard to find in the actual city . If renting a car that is something to thing about.. getting hotels outside cities are more likely to have pools.

Don't know of pools in Rome and Venice.
Just Google it:
The Italian word for swimming pool is PISCINA (plural PISCINE).
In Florence I do, very well since I worked in all of the ones owned by the city (long time ago).
The largest and most famous is the PISCINA COSTOLI. It's located at Campo di Marte, across from the stadium, next to the Nelson Mandela Center. You can see it on google map. It's a huge Olympic type aquatic center. It's open to the public 10 to 6pm, unless there are sports events scheduled.
Along the river Arno, there is another a City pool. The Nannini at Bellariva is on the Lungarno Aldo Moro.
At the Cascine Park you have the Pavoniere. Not sure if the City still owns it, but it's there.
There are other small ones, often part of hotels, but they let the general public use them for a fee.
https://www.visitflorence.com/it/cosa-fare-a-firenze/piscine-a-firenze.html

There are public swimming pools in Roma, my cousins took swimming lessons when they were little. Don't recall the locations, though. Google search would probably turn up something.

We surprised my daughter with Lido Beach. We did not tell her where we were going. She really enjoyed it. I think it was a pebble beach as is common in Italy, not sand. Someone else can correct me.