Hi Amy,
We stayed in all three places in AirBnB in Jan with a family of four. Here are my recommendations
Overall hint. Once you book your stay, pin it in google maps, then explore google maps for restaurants based on the built in price tool (1-4 star price) and check the reviews. Pin restaurants you want to eat in. Also pin sight seeing. I ended up with lists like Rome Eats, Rome Site, Venice Eats, and Venice Sights. This made navigation when I was over a breeze.
ROME
Its a blend between good eating spots and being close to where you want to walk. We had a week in Rome, and walked everywhere apart from the football game at Roma. We stayed near the Spanish Steps. This was a good location, close to great shopping, but food and restaurants were expensive.
Novana was a good area. I personally would not stay in Prati. We walked to an from the Vatican, which was a 40 minute odd walk, I think you would want to be on the other side of the river. For me, I would look for airbnbs in the following neighbourhoods. Trevi, Ponte, Parione, S. Eustachio, San't Angelo. Monti is Ok, but getting a little out of it. Regola could also be considered. A place in any of these neighbourhoods out you in the walking zone.
FLORENCE
We had a week in Florence and stayed right overlooking Santa Croce Basilica and loved it. We chose this area as it was slightly cheaper and had great eats. Florence is very walkable, so I would recommend staying anywhere in the city centre between the Santa Maria station and Santa Croce Basilica. Anything north to Mercato Centrale (I would not stay that far north). We found Florence to be very walkable, so book in the city and you will be fine. Accommodation got cheaper towards Santa Croce and Santa Maria. We loved the Croce side, however, it was a 30 min walk from the train station with our bags (Which I was fine with)
VENICE
We only had 4 nights in Venice, and we stayed based on price and location. We ended up booking in San Polo, on a Calle one street north of the Fish Market. This was a great bustling neighbourhood, however it was noisy. Venice is really walkable. We did Row Venice around Cannaregio, and it was quiet and sleepy. We walked through San Marco and Dorodouro.
The great thing about San Polo is its close to everything, you can access almost anything easily.
Have a look at price, versus location. Remember, there is a lot of street noise in Venice, so if that bothers you, head out to the surrounding suburbs.
We got a four-day Vaporetto pass, and this was excellent for getting around.
Hope this helps, Have a great time planning and a great trip.