I live in Italy and earlier this evening, my landlord halloed outside my window, and when I opened the door, he presented me with a plate of figs he had picked, and they became our dessert for dinner. I could spend three or four paragraphs raving about them, but instead I'll say:
I hang around Chowhound boards enough to see that most questions from people planning a trip focus on seeking the best restaurants, pizza, gelato, and some occasional ones about baked goods, oiive oil, wine and chocolate.
I urge you not to overlook the joys of eating fresh fruit -- instead of prepared desserts, including gelato -- when you are in Italy. And I urge my fellow Chowhounders who are Italy lovers to include in their advice about where to find good eats information about where to find good fresh fruit. In Italy, fresh fruit is often exceptional, bursting with flavor, better than any prepared dessert.
I realize it is a special treat to get fruit picked right off the tree or vine and handed to you, But even the lowliest alimentari (food shop) often has fruits in season that are real "wows" to eat, and almost everywhere you go in Italy, you will find food markets. Don't be shy about telling the vendor you are a tourist and you want to taste the very best.
Where I live, in Liguria, if you aren't staying somewhere where you can pick the fruit of the trees or bushes (not as uncommon as you might think), the covered market in Genova -- the Mercato Orientale on the via XX Settembre -- has many vendors that sell FANTASTIC fruit. I like to walk around the mercato more than once, eyeballing everything before making my purchases. Vendors are more than happy to give you a taste.
I don't know about places like Venice, Rome or Florence, but during the summer here in Liguria, even ordinary family-run stores have marvelous local forest berries, wild blueberries, melons, apricots, watermelons, and especially peaches. We also get wonderful green plums and teeny sweet violet plums. Come fall, fig season really reaches its peak, but we also have fantastic pears (especially giant "abate" pear) and persimmons, both of which last all winter. (Apples are best much closer to the Alps.)
We also get incredibly sweet tangerines and clementines in November and early winter. We all wait for spring and the return of strawberries.
A great many Italian fresh fruits have a density and complexity that has been lost in other countries. I have a terrific sweet tooth, but I have yet to discover the Italian "dessert" or dolci that matches the impact of ripe, fresh Italian fruit.
While you are touring Italy, consider pausing to buy fresh fruit as your afternoon snack, or as a treat to take on your train rides. I don't think you can taste fruit as good as this in many places outside Italy.
Maybe fellow Chowhounders who live in other parts of Italy can add to this post and guide you to some quality vendors or highlight regional specialties that will give you an insight into the fundamentals of Italy as a very, very tasty country.