Rome with a tween

I'd ask the tween! Have a great trip!

If the tween loves history you could easily put together visits to spots that reveal the time period when Rome was a province of France - that is very interesting history.

When Napoleon II was the King of Rome there were so many beautiful buildings and parks built reflecting the refined taste of the French empire:

https://en.wikipedia.org/wiki/Rome_(department)#:~:text=Rome%20(French%3A%20%5B%CA%81%C9%94m%5D,renamed%20on%2017%20February%201810.

for instance, the Spanish Steps and the church at the top of them were paid for and built by Frenchmen:

https://en.wikipedia.org/wiki/Spanish_Steps

I've taken my well-travelled tween and young teen grandsons to Rome and it worked well to go to the Underground Colosseum very early, to St Peter's very late, and to the Vatican Museum very selectively and late. (Early Dec and none too crowded.) The Pantheon was a brief visit, also late in the day when there was no line. Their absolute best times involved food! Testaccio food tour was the highlight, and a couple of dinners at our favorite Trastevere restaurant a close second. Stayed in a VRBO close to Piazza Navona which made life easy.

I travel a lot with friends who can get up, pack up, and move out quickly. With kids it's just not the same. Two days in Rome would be a little hectic for us.

Three full days. Rome has so much to see. You are going to want some down time to wander. You will have none with only two days.
When is this trip? You need to take the heat into consideration too

Enjoy

Any other less-touristy suggestions?

LOL, most of the treasures of Rome weren't built for tourists! :O) Just a couple of ideas?
If your tween is into ancient Roman history, get out to the Appia Antica for a bike ride or long walk (we did it on foot) along some remains of crumbling mausoleums, an emperor's private circus (Villa di Massenzio/Maxentius), 2 catacombs (highly recommend doing one of them) and other interesting stuff. You could also go see the Park of the Aqueducts section of this "largest urban protected area in Europe."
https://www.parcoappiaantica.it
https://www.parcoappiaantica.it/smart-info-ita-eng/
https://www.parcoappiaantica.it/wp-content/uploads/2016/05/AppiaAntica_eng_2015.pdf. (this is a really useful map of landmarks)
https://www.turismoroma.it/en/places/villa-maxentius
https://www.catacombe.org
https://www.catacombesancallisto.it/en/index.php

There are a couple of now-Christian basilicas that retain their original Roman layout. My favorite is Santa Sabina, a climb up the Aventine (free). There's also a nice view of Rome from the orange garden next door. Bring along a snack for a break.
https://www.turismoroma.it/en/places/basilica-saint-sabina-allaventino
https://www.turismoroma.it/en/places/savello-park-or-orange-garden

Baths of Caracalla: for a sense of how enormous these things could be!
https://www.turismoroma.it/en/places/baths-caracalla

You mentioned the Colosseum? Be sure to visit the Forum and Palatine as well (included with your ticket). I highly recommend a tour which includes all 3 as the latter two are more complex sites.

What area should we stay in? Ideally, we'd be in a non-touristy
neighborhood with easy proximity to the sites

I'd prioritize a central location over avoiding other tourists. The bullseye for that is around the Pantheon and Piazza Navona area; you can group your sightseeing from there in all directions.

2 full days or 3?

Three if you want to do the Vatican + Colosseum/Forum/Palatine + Pantheon + other attractions + random roaming around; always a good time in Rome! You know tickets are now required for the Pantheon, right?

We took my youngest to Rome for a week when he was 11 and we all loved it. I would do 3 days. We booked each day a private tour through rometourswithkids.com and our guides were excellent. It made it so much more fun, and honestly efficient, to have guides. We also did a walking food tour through Eating Italy which I think is now Eating Europe. Highly recommend.

I forgot to add, we stayed at JK Place, and it was outstanding. Ideal location for walking to everything, and they couldn’t have been sweeter to our kiddo. One of my all time favorite hotels. Not cheap.

I would plan for three full days if you can swing that. Rome is a big city and it’s nice to have some down time, especially in the summer.

What about Ostia Antica? It’s pretty easy to get to and might fit the bill for your history loving kid. Also I second the recommendation for a food tour. We did the Testaccio tour with Eating Italy a few years back (no kids though) and it was a highlight. Enjoy your trip and be sure to have lots of gelato!

Try the Villa Borghese gardens in the north part of the city, which is a huge park with historical sights, beautiful gardens and areas to spread out. We were there in May 2024 with a 13 year old. We rented bikes and explored the park for hours. We wished we had more time to explore. The bike rental company is called Bici Pincio and is located near the entrances. They have e-powered bikes that were reasonably priced.