In Venice there are no roadways or cars, only canals and water taxis, so a car seat is unnecessary. When we traveled to Venice the only time we got in a vehicle was when we took one of the buses from the airport to the water taxi station and you are unable to install a car seat on the bus. Venice is full of bridges and crowded cobblestone roads you will end up taking the baby out of the strolled many times to climb up and down the stairs and it may be difficult to navigate through the crowds during the busy times of the day. I was 3 months pregnant when we traveled to Venice and I managed to carry Jordyn (15 months) with my Ergo 360 carrier just fine.
We did the Secret Itineraries Tour at Doge's Palace and strollers are not allowed. It would also be hard to bring anything bigger than an umbrella stroller on a gondola ride. The Islands of Murano and Burano were probably the only places I feel like it could of made any real sense to bring the stroller but I managed fine with the carrier alone.
Now there is a lot of walking in Venice so if your child can't make it through the day walking on their own and you know you personally can't manage carrying them in a carrier all day then I would bring a cheap, very small umbrella stroller. Anything heavy and bulky like a travel system or jogging stroller will be a real pain as you will have to carry the stroller up and down the stairs of the many bridges located throughout the city.
Florence: Stroller and Carrier
Florence is a regular city with with cars and sidewalks, although narrow, so a stroller is a good idea here. I still recommend a smaller umbrella stroller as it is just easier to navigate the streets. Keep in mind if you are renting an apartment through Airbnb or similar service these buildings may not have an elevator so you would have to carry the stroller up and down the stairs. In our Florence Airbnb rental we were on the 5th floor and what I would not have wanted to do was carry a heavy stroller up and down multiple times a day.
I mainly used the stroller in Florence but there are some places like the Gothic Cathedral we visited in Siena our a day tour where strollers are not allowed and you may find your carrier useful. This is also the case if you plan to go to the top of Duomo's Dome as there is no elevator and 463 steps to the top.
Florence is very walk-able and we didn't see the need to get in a cab once. The day tour we did was on a tour bus and we wouldn't of been able to install a car seat so it would of been useless for us.
Rome: Stroller and Carrier
In Rome I recommend both your umbrella stroller and carrier. I used the carrier while on the tour of the Colosseum but a stroller could work great here as although two levels there is an elevator and a train station directly in front. Had I known that before doing the tour I would have used the stroller this day. If you are going to the Vatican strollers are not allowed inside, you will have to leave it at coat check, so be sure to bring your carrier as the tours are lengthy and crowded and it's great for when baby/toddler wants a nap. We didn't get in any cabs while in Rome as their public transportation is great and if somewhere wasn't walking distance we took the train or bus. Unless your renting a car I think the car seat is useless here as well. We did do a day trip to the Amalfi Coast and Pompeii but again we took a tour bus so we would not have been able to install the car seat anyway.