I'll be studying abroad in Italy this summer and I will be traveling after. Because of this I will most likely have an extra bag with me. From what I've seen it is pretty expensive to ship a bag back to the states. Are there places I could store my bag (possibly at a train station?) at a reasonable price for about 3 weeks? And then circle back to get it before I fly home.
Yes, you can store them at train station for sure. Depends on size of the bag though.
If you are renting a room where you study, ask the owner about storing your luggage.
If you are going to store your bags for 3 weeks, you should shop around for the best price. It will be costly in most places.
Price the cost of a locker in the RR station or air terminal you are in. If I don't find a locker I go to the nearest hotel and ask the concierge.