Cathedrals

Florence Duomo from the outside, the interior is unremarkable
Santa Croce for the famous people tombs, Pazzi Chapel, Giotto frescoes
Santo Spirito in Oltrarno-Michelangelo’s crucifix
Santa Maria Novella for the art

Venice St Mark’s Basilica and Frari Church

Bologna Duomo was interesting but probable skippable
The group of churches Santo Stefano etc

Rome St. Peter’s Basilca and a number of other chuches-all free-all worth a peek, and of course the Pantheon

We liked Basilica di San Domenico in Bologna.

https://www.bolognawelcome.com/en/places/religious-buildings/basilica-di-san-domenico-en

Adding to the one's Christine mentioned.

There are countless must see churches in Rome, these are a few:
- Santa Maria Maggiore
- San Giovanni in Laterano
- Sant'Ignazio 

Florence:
- Santa Trinita
- Santa Maria del Carmine

Venice:
- San Giorgio Maggiore
- Santa Maria della Salute

Bologna:
- None are must see

Remarkable advice thank you to all

We rarely pass by a church without taking a quick look
They are free (most), usually not crowded, a cool quiet space to get away from crowds and heat and rest your feet for a bit
Anazing art in most every one

Another vote for Florence Duomo exterior vs interior. Santa Maria Novella is criminally underrated by comparison. Ghirlandiao’s frescoes are only overshadowed by his pupil’s. There’s several other works in there that adorn every art history book.

Rome’s smaller churches are where it’s at. Even the ones that don’t have a Caravaggio or Bernini can be incredible to visit. Pop into any you see.

Some of the smaller churches will be closed for a few hours in the afternoon
If there are any of particular interest to you be sure to check those hours

Two of my must see’s in Rome, not Cathedrals but important and historic churches, are Santa Maria and Santa Cecilia, both in Trastevere. Both trace their founding to the early Christian period and both have stunning examples of early medieval mosaics, traces of their Roman origins and painted frescos.

After a lot of overly decorated churches, I really enjoyed St Paul’s Outside the Walls, which is part of the Vatican. The original church was built around AD400 and destroyed by a fire in the 19th century. The “modern” building we see today was built in the general style and following the footprint of the original. The vast interior is relatively empty with a few remnants, a mosaic, a candlestick, and a marble canopy rescued from the older church. Around the interior are mosaic portraits of all the popes. This Basilica also houses the supposed sarcophagus of St Paul. Bought some superb limoncello with the papal seal on the label at the gift shop!

This doesn't answer your question, but if you're a lover of cathedrals, you should try to fit in a 1/2 day visit to Orvieto. The cathedral there is spectacular.

Referring to “cathedrals” might be a bit confusing. A cathedral doesn’t just mean church. Cathedrals are the seat of a bishop. There is normally no more than one (if that) in a city. The most impressive church isn’t always the cathedral. Examples: Rome’s cathedral isn’t actually St. Peter’s, but San Giovanni Laterano. St. Peter’s is a basilica, another kind of special church, but not a cathedral. The Italian word “duomo” is usually a cathedral, but not always. In the four cities you list, if you have to see just one church, it’s Venice San Marco; Florence Duomo; Rome St. Peter’s; and Bologna San Petronio (not a must see compared to the others, but Bologna is a great city). Of course there are many other very worthwhile churches in those cities and elsewhere in Italy.

In Venice, the St. Marks After Dark tour is amazing. Expensive but worth the spend to avoid insane crowds and see things they won’t.

Technically, each city only has one Cathedral, at most. It’s the home church for the local bishop. There are significant churches that don’t have a bishop at present that would be worthy of the title. Those are generally called basilica.

I assume you're using the term cathedral to refer to churches and basilicas, too.

Bologna:

• Santuario di Santa Maria della Vita for its breathtaking polychrome terracotta sculpture, Lamentation over the Dead Christ (circa 1463-1490, Niccolò dell'Arca).

• Basilica di Santo Stefano for its unique design, relics and historical importance. Known as Complesso delle Sette Chiese (Complex of the Seven Churches).

Thank you everyone for the advice and the lesson on cathedrals and churches. Sorry for my ignorance when it comes to this. I appreciate everyone’s kindness and suggestions

Just one more clarification of my previous comment about normally no more than one cathedral in a city. That's assuming we're talking about just one denomination, the Catholic Church in Italy. If another denomination has bishops, they may also have cathedrals. A non-Catholic cathedral is very rare in Italy, but not unknown, for example, there is a Greek Orthodox cathedral in Venice in addition to the Catholic San Marco (St. Mark's). Multiple cathedrals in a city are more common in a country such as the UK where the Anglican church has cathedrals (virtually all of the big, famous ones), but so does the Catholic Church. And a big city may have more than one diocese within the same denomination, such that London has St. Paul's Cathedral on the north bank of the Thames and Southwark Cathedral on the south bank, both Anglican, plus others.