Luggage stores are everywhere, but it depends a bit on where you are. Are you in Rome? Venice? You can find inexpensive luggage everywhere. Whatever you do, don't buy anything in the street. That would be counterfeit stuff designed to break before you get to the airport, despite the fake Gucci label. If you just want luggage to get home, any store will do. If you want luggage to last for some years, then no on can tell you where to buy luggage today, because you haven't told us where you are. Italy is a whole country, with big towns, small towns, and everything in between. It won't help if I recommend Rinascente in Rome or Torino, if you are in Bari.