Storing Suitcase in Florence or milan

Why are you carrying a large suitcase that you don't need?
Maybe you can do without.
Unfortunately the deposito bagagli at the stations do not accept luggage for such long term. I think the max is 10 days.

We will be traveling after my daughter finishes studying there so need to store her things before coming home. The school provides no options for this problem. We are going thru Milan airport twice so that is a posibility if they have a bag check for 10 days (cost?). Thanks. for replying.

Even worse, Rick's research says that the baggage check at Milano Centrale stations is for maximum 5 days. If you have a hotel booked for your return to the city, then they may agree to hold the bag for you. http://www.milanomalpensa-airport.com/en/services/banks-and-services has a phone number for the airport bag storage; your daughter could try calling them from within Italy.

I don't know what the time limit is in Florence (S.Maria Novella) but it's probably 5 to 10 days max also. In addition the daily rate is about €16 therefore, even if they allowed it for 2 weeks, that would be well over €200 so I wonder if at that point it might be worthwhile to ship everything back to the US. I'm assuming that after you all go on your 2 week trip you all return to the US.
Also if your daughter is studying in Italy (probably Florence, since all Americans seem to be studying in Florence), she might have some connections (friends or even the school or where she's staying) that could hold her stuff for 2 weeks).
I know of a baggage storage service in Rome. They would probably hold it for you for a longer time, and they pick it up and deliver it back to you wherever you want (hotels, airports etc), but I believe the operate in Rome only.
You can check with them and see what they say, maybe they know of a similar business in Florence:
www.bon-bags.com/
Or Maybe you can make Rome your first and last destination of your 2 week travel plans before heading to the airport where you depart from .