Best most central area to stay in Rome, Florence and Venice.

https://store.ricksteves.com/shop/p/italy-guidebook
https://store.ricksteves.com/shop/p/best-italy-guidebook
https://store.ricksteves.com/shop/p/pocket-venice
https://store.ricksteves.com/shop/p/pocket-florence
https://store.ricksteves.com/shop/p/pocket-rome

Look for these at a library if you do not want to buy them. Should provide a lot of info to help you plan your trip.
https://www.ricksteves.com/tours/italy/venice-florence-rome

You do not say how long you have , but this might give you an idea of scheduling. Note that the tour has a dedicated bus and guides who don't get lost, so you probably cannot cover as much on your own, in the same amount of time.

There is a great deal to consider as to neighborhood in all three and I have to concur with Joe that a guidebook is a great place to start. What I love about the Rick Steves’ guides is how the neighborhoods with pros and cons are explained in a way no other guidebook I have read does. You don’t necessarily have to use his specific hotel recommendations but the neighborhood info is invaluable.

Based on Rick Steves’ advice, and confirmed by stats in those cities, we now look for areas just outside of the absolute central (and most crowded and expensive) areas. They’re still very close to downtown attractions, but have a less crowded, touristy, and pricy aspect, along with their own outstanding restaurants, markets, etc.

In Rome, there’s Trastevere, on the west side of the a tiber River, across from the more central part of the city. But even better is Testaccio, just south of Trastevere but on the east side of the Tiber, in what used to be Rome’s meat packing neighborhood. It’s just west of Circus Maximus, and just north of the Piramide Metro station.

In Florence, it’s another neighborhood across the river, but this time, it’s west of the Arno River, and it’s the Oltrarno neighborhood.

In Venice, go for the Ghetto, just north of St. Mark’s (central) Square, or Arsenale, just to the south.

Know it's always best to fly INTO VENICE and OUT OF ROME. Flying out of Venice is difficult. So fly into Venice, train to Florence, train to Rome, fly home. We just returned from 3 weeks in Italy -- we go often - it's our fav European country. If you need private guides for your 3 towns, let me know - we had some amazing ones.

Venice - we like to be near the canal, near the Rialto Bridge - - we LOVE LOVE LOVE -- Al Ponte Antico - they even have a private dock so you can take a private water taxi from the airport and they drop you off at the hotel so you don't have to deal with luggage on the Vaporetto. It is a palace from the 1500s - only has 9 rooms - the owners are amazing and make the BEST breakfast. The offered great restaurant recommendations for us. They book up VERY fast. Def see St. Mark's Basilica- best with a guide. The Jewish Ghetto also good walking area. Get the Rick Steves Venice Pocket Guide.

In Florence - we like to be near the Duomo or Piazza della Signoria. We don't like the other side of the river other than to visit.

Don't miss the DAVID (best with a guide), The Duomo & Baptistry, and Santa Croce Church - it is stunning and more impressive than the Duomo. We did a 2 hour FREE tour of it with Dan Harper who volunteers there and gives free tours - let me know if you want his email. It was fantastic. Get the RS Florence Pocket Guide.

In Rome, we like to be near Piazza Navona or the Pantheon. Don't miss the Vatican, the Colosseum/Forum, San Clemente Church (our favorite - on 3 levels from the 1st Century, the 4th Century, the 12th Century - the history is insane and it is so overlooked - it's the local's favorite and the guide's favorite), The Pantheon - all best w/a guide. Get the RS Rome Pocket Guide.

Know that 2025 is Jubilee and crowds and prices will be crazy and most locals and guides recommend NOT to come to Italy then.