I just came back with my teenaged girl last week. It was amazing, and she loved every second. We bought a timed entrance to the Colosseum for 3:30pm the day after we arrived, and usually this gives you up to 24 hours before or after the timed entry to visit the Forum. So, once we checked into the hotel, we showered and went out to the Forum. We went into the side entrance, and because it was later in the day, we were the first in line and went right in.
Some things I didn't see mentioned that are 100% free:
The four-basilica pilgrimage tour: Santa Maria Maggiore, Saint John of Lateran, Saint Paul outside the Wall (we took the Metro from Cavour), and of course you'll do the Vatican on Saturday. We're not Catholic, but all of them were beautiful, full of art and incredible architecture...and important to Christendom. There's a cloister at St. Paul outside the Walls that has incredible relics and ancient statuary. The gardens are also beautiful as you exit. While we were at St. John of Lateran, we dashed over to the Santa Scala. We didn't climb up on our knees, but there is a fabulous little gift shop at the top that sells handmade goods and goodies (we got a fun lemon cookie and orange-scented chocolate chip cookies made by nuns from a local....convent?...and they also had honey and other neat treasures).
One evening, find Giolitti's gelato shop (Amarena--black cherry!) and then walk over to Castel St'Angelo. Make sure you cross the bridge and continue along the Tiber River to the Supreme Court building and cross back. There is something magical about Rome in the dark. They have mastered the art of night lighting. Every single picture came out amazing. It was also incredibly safe. The police were everywhere, and as two females traveling alone, it felt incredibly reassuring.
I hope you plan a skip-the-line tour of the museums in Florence. We went in winter and were still so glad we did. The guides made the art come to life and helped us to understand what we were seeing. This should help your teens tune in if they aren't art and history fans. Rome will spoil you with its beautiful architecture. I feel like Florence hides its beauty inside buildings, so walking around isn't the same feast for the eyes. And definitely hit up Gelateria La Carraia on the other side of the Arno (their pistachio is decadent). Of the nine places we tested, it was our favorite.
We thought about a food tour, but instead we opted for a seven-course tasting menu at a restaurant in Rome. It took 3 hours and was some of the best food I'd eaten in my life. Without wine, it was way cheaper than any food tour we saw advertised. Make sure you get burrata somewhere. We had it two different ways in Florence (once with fresh truffles, another time smoked) and were hooked.
