You don't say where you are going in Italy, or how you will be getting there beyond the plane. Just remember that if any kind of public transportation is involved, you will be schlepping that luggage to, from, on and off it. And depending on where you are staying, you may be carrying it up and down stairs yourself.
Apocryphal tale: We spent a month in France in June, 2012. We started with 8 nights in Paris. The 2nd night we went on a Seine dinner cruise. All the advice said to "dress up," so we did. My husband wore a pair of nice slacks, a nice shirt, a tie and a jacket. We bought that stuff specifically for that trip because he owned nothing even close to that and we (mostly me) thought he would use it that night as well as for other nice dinners out in the evenings. The ONLY other people dressed up on the boat were a group of Japanese women. No men speaking any language were as dressed up as he was. He carried that "outfit" the rest of the trip and never wore any of it. As a result, he will never bother packing anything like that again. He looks and feels much better in jeans or twill pants, and hates ties and jackets. They just aren't him.
Sidebar about me, since some other women have mentioned what they wear: I wore a 2 piece dress that night. I used it only one additional time on the trip. So it also did not fit the "don't take it unless you will wear it at least 3 times" parameter of smart packing. I should've known better. Even on my first (4 month long) trip to Europe in the late 70's, I never wore the dress I took. I look and feel much better in pants than in a skirt of any length.
Obviously, neither of us are "casually dressy" people and feel very uncomfortable dressing that way. We never had to do it for work and we certainly don't do it now that we are retired. We also never wear shorts at all, even here in hot, hotter, hottest AZ.
If you are more comfortable, wearing shorts and dressing somewhat dressy, go for it. But don't expect that you will look like a local in Italy. In my observation that's more about attitude and personal style than it is about clothing.
And as others have or will mention, the most important thing you can pack or wear is a pair of VERY good walking shoes. Shoes that you can walk or stand in for hours, over cobblestones and on hard surfaces. You will walk and be on your feet far more than you can possibly imagine.