There will be crowds all around the most popular and famous sites --- there is really no avoiding that, although early morning and evening visits will help. We were there 10 years ago from December 21st to December 31st and it was plenty crowded then and now more so since COVID. The Christmas lights are lovely at night, and people will be out and about, and eating dinner at about 9:00pm, so it's fun and safe to be out at night.
I am glad that you are staying in the Oltrarno --- that will help you feel not so much in tourist-land. Just keep telling yourself "These people are here for the same reason we are, because Florence is one of the greatest places to be on earth."
In addition to that December trip, we have since stayed in Florence for 70 more days (with only 4 day trips), so we have seen a LOT. Our latest trip was last November. I am thinking about the teenagers in making the following recommendations.
Find the flood markers from the 1966 and previous floods high on the walls --- some on streets, some in the courtyard of Santa Croce, one is inside a shop. Before you go, read "Diary of Florence in Flood" or at least the first several chapters. Written by someone who was right there, seeing it all happen, staying in a guesthouse next to the Arno. Her book has been reissued recently under the less good title "Florence: Ordeal by Water." You can see videos of the 1966 flood on Youtube.
Eat lunch in the Sant'Ambrogio market if you are over in that area.
Bardini museum --- collection of art & artifacts in a 13th century building made into the collector's home. Nice collection of armor and weapons. The last time I was there, only a couple other people were there. At the top of the gardens behind the museum there's a great view of Florence.
The Palazzo Davanzati will need tickets and you have to be led around by a museum guide, but it's really interesting to be inside an old palace.
Duomo museum --- A world class museum that is not crowded. It's one of my favorite museums, but I enjoy church art. The actual doors of the Baptistery are there. If your group has seen enough of church art, you could skip it, though.
The interior of the Duomo and the frescoes inside the dome are, in my opinion skippable when on a short visit. I've never done the climb, but I've done other climbs that were very cool, so I would guess that this one is, too.
Museo Archeologico Nazionale --- If anyone likes archeology, otherwise you could skip it. I love this museum!
Baptistery --- If the interior mosaics are still being restored, perhaps do the expensive scaffolding tour to see the mosaics up close. One of the coolest things I've done in Italy. If the restoration is going on, but you don't want to do the tour, be aware that the mosaics are hidden by fabric below the scaffolding.
La Specola --- I expected to dislike this natural history museum but loved it. The teenagers will like it, I think --- a lot of weird, weird stuff there.
Try to see the Benozzo Gozzoli chapel in the Palazzo Medici Riccardi --- a tiny room where you could easily spend an hour (but you don’t have to, unlike most of the other churches, museums, & art galleries) looking at all the details of clothing, portraits of the Medici family, animals, horses, flowers, etc. I always skip the rest of the palace. The paintings covering all the walls seem to be saying “We Medici are like the three wise men bringing gifts, so it’s OK that we are filthy rich.” The room fills with people and empties every few minutes.
Look for Clet Abraham’s clever altered street signs. And lots of other street art!
I've never been to the Pitti palace and never wanted to. Was not excited by the Boboli gardens, either (and I am a serious gardener!). Very skippable when you only have a week.
The view from San Miniato al Monte is wonderful and free!
Have a terrific time!
