Thanks for all of the wonderful recommendations! I have so much to consider now!
Oltrarno, sounds like a good option for me too. My daughter is hearing that most of the time the FUA study abroad student apartments are on the other side of the Arno so it might be practical for me to look closer to there since you mention there is also a market place close by.
Apartments with stoves are not plentiful so I am considering booking one near San Lorenzo and another in Oltrarno so I don't loose out and then just cancel one when she gets her housing address in August.
I had looked at some really beautiful places in Fiesole at one point and the area did look really beautiful. Was the #7 bus a long ride? How often did it run?
How was the weather when you were there last year?
I am so glad I found this forum! Other than a trip to Bermuda last March, I have never travelled beyond NE so it is great to have all of you seasoned travelers offer such great advice! Thank you all!!