Attractions in Italy that may require pre-booking before arrival

T he list is long. Purchase a good guidebook or visit your local library. You might consider checking out DVDs to help refine your interests as to what is needed in advance.

There are dozens of worthwhile sights to visit in each of your locations

You need to narrow it down and give us your list as we have no idea which are your priorities

Just a few for sure
Rome-Colosseum, Vatican, Borghese, Pantheon
Padua-Scrovegni Chapel
Venice-St Mark’s Basilica, Doges Palace
Milan-Last Supper, Duomo terraces

You need to do all the research. Buy or go to a library for a good guide book for Italy.
Or, best way, Google each historic site you are considering visiting.
For example, Google “the Colloseum” and it will tell you whether you need advance reservations
( you do!) Google will be the easiest and most up to date way to research the answer to your question. Planning an independent trip takes a lot of time and finding answers to the questions you asked is part of your necessary research.

Christine mentioned most of the places I'm aware of as a result of either visiting or planning visits to Rome, Padua, Ravenna, Venice and Milan recently. You can add these:

San Clemente in Rome: Doesn't sell out super early. Was selling zero tickets in person as of March 2023, but that may have changed in the meantime. I don't think you need to buy the ticket particularly early, but April would be busier.

Domus Aurea in Rome: Limited tour slots available. Books up early.

Guggenheim in Venice: I twice saw a bit of a line at the Guggenheim. Judging by the number of people inside, it is very popular. I didn't run into a sell-out, but there's no sense in going over there to stand in a ticket-buying line, not knowing what entry time you will be given. By contrast, it was not a problem to walk right up to the Accademia in Venice and buy a ticket as of September 2022.

Also in Venice: There's a rooftop viewing platform at the Fondaco dei Tedeschi near the Rialto Bridge. It think it's free, but you have to pre-book an entry time.

Ravenna hasn't been swarming with tourists on either of my two visits (2015 and September 2022), but crowding must be a concern at times, because the combo ticket covering some of the major mosaic sites specifies entry times for two of them, I think. I really don't know whether it's ever essential to get that ticket ahead of time.

Also if you will be traveling April 25th a national holiday or April 30th the day before a national holiday you may encounter more Italians traveling so keep that in mind. The May 1st holiday that bridges with April 30th is very popular.