My DH and I visited Florence for three days a month ago.
Super easy to get from the airport into town by tram.
We stayed at a pretty expensive (for me) place, but I loved it.
https://www.airbnb.co.uk/rooms/1385593767997829492?sourceimpressionnid=p317505893388P3QmQRA9NlSt4CwA
They rent out 4 rooms, there's a shared kitchen and a shared terrace.
We had one of the two rooms out front which was gorgeous.
Somebody who worked there recommended two places to eat which we LOVED.
Alla Vecchia betolla - we went for lunch and it was about 1/4 tourists and 3/4 Italians on their lunch break. You share tables and it's lovely and informal
The other place il Santo bevitore - had another amazing meal here. Highly recommend. When we went you had to pre book restaurants in the evening (or be prepared to wait in line), which I didn't like that much, but maybe October will be less busy.
Roughly - on one side of the river you have the Uffizi, academia, duomo, the place where we stayed, etc which is gorgeous but very touristy.
The other side of the river (where both those restaurants are) still has a fair share of tourists, but feels a bit more like "this is where people actually live"
I would think staying on that side of the river you get better deals on hotels.
We pre booked Uffizi and academia which was great. Duomo is stunning from the outside, but not so spectacular on the inside. We climbed the Giotto tower next to the duomo which was fun. I think the climbing the actual dome of the duomo, rather than just going inside must be really interesting (we didn't get a ticket for that)
I never felt unsafe, but equally was careful with my things.
What an amazing thing for your daughter to do. Have a great time!