Is there a storage location at the airports and train stations where extra luggage can be stored for a few days? And how much will the storage cost?
The answer is yes,no or maybe. There is not a universal answer to your question. Which train stations, which airports, etc???? Do some homework on your own by checking web sites and then come back and ask about specific locations.
Sam, the rail stations charge Euro 4 for 5 hours, then (I think) 60cents per hour extra. I think RoninRome has a link for a previous question which may give more information.