Planning trip help.

this is a surprise for my adult children.

You have a way to confirm they will have current passports at the time of the trip?

How many nights do you have in Italy?

Look at the 'itinerary' tab for this tour to get an idea of how it might work
https://www.ricksteves.com/tours/italy/venice-florence-rome

Or to eliminate the confusion and overwhelming stress and sign up for the tour, since it goes everywhere you want.

As usual with this kind of question, there are a few good answers, including "It depends."

If you are traveling by train and won't have a car, you will want to stay in an area of each city that is easily accessible from the train station and also convenient for whatever sightseeing you like to do. A lot depends on how far you are all capable of walking with your luggage.

Venice
Here's a good website that outlines the six sestieri (districts) of Venice. It might help you decide. http://www.about-venice-travel-guide.com/sestieri-of-venice.html

Be sure to consider whether you want to sleep somewhere quieter and a little away from the tourist areas, or if you'd like to be in the heart of things.

Staying fairly close to the Grand Canal makes it easy to take a vaporetto from the train station to your lodging and to get around.

Florence
The train station is pretty much within walking distance of all the historic sights in Florence. I'd look for a place within that historic area, assuming you area all capable of walking. I stayed in this B&B: http://ilsalotto.difirenze.eu/. Nice place, easy to walk from the train station, and literally around the corner from the Duomo.

Rome
I'll leave this to someone else, as I have not been to Rome yet.

Venice: we recently stayed to the east of St. Marks., near Chiesa di Sant' Antonin. It was a nice, quieter, less crowded area. We would definitely stay in that area again. It's nice to be able to get away from the crowds.

Florence: We recently stayed just across the Arno, very near the Ponte Vecchio. It was very loud until late at night. There were some unhappy locals near us yelling and arguing late into the night (every night), making a good night's rest very difficult. Then, after sleep was finally achieved street vendors woke us up before daylight each day by rolling their ridiculously noisy motorized vendor carts up the cobble stone alleys toward the piazzas to start their day. Even though the apartment we rented was absolutely perfect, and our host was amazingly helpful, I wouldn't stay in that area again.

Rome: We rented a small apartment in Trastevere for my last visit to Roma. It was a great area with lots of wonderful restaurants. (Some not great tourist traps as well). I'd stay there again. On previous trips, I stayed near Termini and in the area known as Monti. No complaints about either of those areas.

Rome locations I recommend are Prati (near the Vatican and well connected by public transportation as well as largely walkable to the historic center), or the area near the Pantheon/Campo de’ Fiori/Piazza Navona (atmospheric, walkable, good bus connections, restaurants abound).

Rick Steves’ guides give great info and advice on where to stay and why. Do you have the Italy Guidebook?

I usually peruse the RS itineraries on his website and then check out a guidebook from the library (or buy it). Someone's definition of 'good' may not be yours...including Rick Steves!

For a fairly good description of the neighborhoods of Rome read this.

https://theromanguy.com/italy-travel-blog/where-to-stay-in-rome-this-year/

I have a hard time picking my favorite, for ease of transportation, Monti and Prati (closer to Piazza Navona). For charm Trastevere and Campo dei Fiori. Taxis and busses easily reach other areas.

Venice...I like the Arsenal area. Quieter, but vaporetto within easy reach. Very walkable to most sites.

Florence...across the Arno beyond the Pitti Palace. Or by Santo Spirito.

Curiously, we are not yet hearing from the OP?
OP, what about the passport question in the first reply?
We want to help, but for us to be more helpful, it would help if you would interact with the people trying to help.

First, if you want an apartment, don't just look at Airbnb. Look at other sources, such as HomeAway and VRBO.

Second, I like the EuroCheapo website. Their descriptions of neighborhoods in various cities are useful - even if you aren't interested in "cheapo" accommodations. Here's their description of neighborhoods in Venice https://www.eurocheapo.com/venice/hoods/, Florence https://www.eurocheapo.com/florence/hoods/, and Rome https://www.eurocheapo.com/rome/hoods/.

Third, I do agree with looking at Rick's books. He always highlights his favorite neighborhoods to stay, and lists local sources for apartments.

If you want specific recommendations, you need to tell us your budget and specific requirements. We know it is 6 adults, but how many rooms, bathrooms, and beds do you need? Can you walk up stairs or will you need or want an elevator? Do you want a certain view? Etc.

Thank you for your responses. My daughter was in town and is a little noisy so I didn't look at any trip stuff.

We all do have updated passports.

I am really looking for a clean place to sleep as a home base. We are all very active and will want to be out exploring.

How many bedrooms/beds do you need? Likewise what is your budget per nite.