While you could probably find something called “granita” in different parts of Italy, the original recipe is from Sicily, and even here you can get very different versions of the same product depending on the province or the town. This is due to the different freezing techniques that are being used: the smoother types are produced in a gelato machine, while the coarser varieties are frozen with only occasional agitation and then scraped to produce separated crystals (so the granita is more similar to ice).
On the east coast of Sicily, the Sicilian granita is smooth as a sorbet, and is normally served with a brioche (better if a warm one). It is wonderful for breakfast, but during the hot season you can enjoy it all day long. Most pasticcerie and bar will offer you quite a wide range of different tastes, from fruit (peach, lemon, strawberry, black mulberry, almond) to chocolate, pistache and coffee.
Our special advise for a great granita: try a mandorla granita with liquid, hot coffee on top and a brioche. Simply delicious.
Read more about Granita on wikipedia