Where do the children go (Rome and Florence)?

Have your son climb the Duomo's Bell Tower in Florence. After that, you will be looking for a bench for him to rest. 😀

Its a bit outside the main city, but there is a lot of green space around the aqueducts in Rome. You can see the aqueducts and combine it with running around.

He can run and play to his heart's content in the Villa Borghese in Rome. It's the big park at the top of the Spanish Steps, not the museum of the same name. In Florence, take bus #10 from Piazza San Marco out to the soccer stadium, where there are parks where he can play. If you go outside of school hours, he'll likely meet some new Italian freinds. Best not to go on Sundays when there's a home soccer match, unless of course you want to attend. Series A soccer is awesome.

In Rome my first pick would be the Borghese Gardens.
Have him ride bikes or row a boat on the small lake. Rentals of these two are available, as well as golf carts. Open spaces abound for a run or booting a soccer ball.

In Florence, Boboli gardens, which has an entry fee, has lots of paths and stairways and an overlook that's beautiful.

Pack a picnic, if allowable, and spend at least half a day at each.

Both are beautiful.

Below are the only places inside the historical center of Florence. Other than that, you need to go a bit farther outside the center (like near the stadium or along the river, or other places but more to the periphery of the city, away from the city center.

Cascine Park

In the same park, also the Club Sportivo di Firenze

At the park on Piazza D'Azeglio, there is a small soccer field (indoor soccer, but outdoors).

At the Terzo Giardino Park, that's Florence beach, cum beach volleyball (summer only, rest of the year it's underwater).

In this specific lawn of the Boboli Gardens we used to play soccer as kids. Not sure they allow that anymore.

He can run and play to his heart's content in the Villa Borghese in
Rome.

Ditto this suggestion. We watched a young man and his dad kick around a soccer ball one morning on our way to Galleria Borghese. He absolutely can play to his heart's content there! We also watched children play near an outdoor bar in Parco Colle Oppio, just a couple blocks east of of the Colosseum. Some further areas of that park can look a little rough but this part was fine, and the (all Italian) kids had fun while the grownups enjoyed coffee, wine or other beverages. It's one of our favorite little corners to collapse in at the end of a long day.

It's on the southeastern-most side of the park, a little southeast of Piazza Martin Lutero, and just a titch north of Viale Domus Aurea (street). It'll show as "Chiosco di Nunzia" on a google map; look for the white, octagonal roof in google earth mode.

There is a small garden park on the Aventine Hill, on the way to Santa Sabina.

I have added these to our google map -- thank you so much!!! One of the first stops we make off the plane will be to purchase a ball :-)

I must chime in to agree with the recommendation of the Borghese Park. It is Rome's Central Perk filled with Romans and their families - footballs( soccer) everywhere and lots of gelato!
In Florence one of my favorite sights is outside our rented flat on Piazza Santa Maria Novella - in the late afternoon and early evening the piazza becomes a small makeshift football pitch - lots of local kids running and kicking around their balls in makeshift games - not very much grass but lots of laughter and enthusiasm. I great place to meet the people of Firenze. The view of the sun setting behind the church is priceless.

Forgot to add, at the little park I mentioned, many Italian children play, and there are great views from the terrace.

And I'll revise my previous recommendation some. Thinking back, most of the kids were rolling 2-wheeled scooters around the nice, wide paths near the bar so it might not be the best place for soccer. Scruffy grass, too, although that's pretty standard in Roman parks. Go to Villa Borghese; lots of room! You can rent 4-wheeled pedal bikes there as well.

Where will you be staying in Rome? Maybe Villa Borghese isn't the closest park to your accommodation, and something else might be literally around the corner to where you're staying. I usually recommend places like Villa Torlonia or Villa Paganini - filled with locals while still super-close to the center of the city.

I did a google search for "things to do with children in Rome" there are at least a dozen links to sites and lists of things to do and see.

We are staying in Piazza Navona.

There is an Italian app called Playground Around that should have decent coverage in Rome. You can ever your location and it tells you where the closest playground or park is.

We just returned from Italy with our 9 year old. Borghese Gardens is a great place in Rome to run and play. Also, we ended up doing Gladiator School in Rome -- I wasn't sure if it was going to be cheesy or fun, and even asked here on the forum for some advice about it. I looked up some pics from it on a blog, showed them to my son, and he asked to go. He loved it! He got to learn to fight with the weapons, throw a javelin, and play-fight in the ring. For adults, I think it would be completely hokey -- but he LOVED it and said it was a highlight of his trip. He went to school today talking about it!

@mom2eandb - perfect! I have downloaded the app -- thank you!!

@Dana - we are doing this as well! I was hesitant also due to some of the comments made here, but my kids are already well versed in light saber play and I thought this was right up their alley. So glad to hear you all had a good experience!!