I have lived here since 2008, and I can say that I have seen almost nothing at all! You would think that if you live here, you get to see a lot of Italy, but as Chillout said, you end up just seeing the city you live in and that's it...
I only started to see small regions recently. Until now I have been to Genoa, visited it a bit, it's beautiful! I've been to the seaside, but only in the West, I haven't been to see Rimini or anything on the East part of Italy yet.
I've been to Lake Garda, visited it a bit, but not much (I plan on visiting more location around it this year, just as the weather becomes warmer).
I've seen some cities, like Milan or Parma and small cities in between... but didn't visit them as a tourist, I've had things to do there and just visited them "on business" so to say.