Yup, sending your stuff home is an option and a good one, although that will be expencive to send 2 duffles and a lap top...I would contact the post office to see what the total cost will be if its with in your budget then send it cause that is really the best option.
Try and contact some hostels in the city who might be able to store your stuff for ya for a cost, but how secure they will be is an issue, i would not leave anything of value (laptop) is a hostel ever. MOst luggage storage areas are accessed several times a day and sometime not by hostel staff.
And my third option for ya is Self Storage,
City Self Storage opened its first Italian location recently and its in
Padova which is kinda far from were you are at about 3 1/2 hour drive, but if ya know someone with a car you could be ok.
Hope things work out for ya, and let us know what happens!