You didn't say where you are landing. Milan? Rome? Venice? That will affect how you structure your visit.
I fell in love with Venice at first sight, walking out of the train station and seeing the Grand Canal at my feet. See it before is totally overwhelmed and sunken. Probably going to have a tourist fee. Get a multi-day pass to ride the "water buses" and go to the other islands, or even something we did--entirely circled Venice on a vaparreto.
Spent about 10 days in and around Varenna on Lake Como, took ferries almost every day, loved the area. Lots to see, great gardens. The other lakes have things to recommend them also.
From Varenna--but also do-able from Milan--we caught the trains to St. Moritz, Switzerland. Lovely trip, also in September. Discovered Laderach Chocolate in St. Moritz-branches in Europe and a few in USA. Best dark chocolate I've ever had.
Milan has a lot to offer, can definitely recommend the Duomo tours (including the roof if still available). Fees charged, but worth it. Some of our group went to the Canal District and enjoyed it.
You can drive to Switzerland from northern Italy, Haven't done it myself, but if that fits your car rental period, something to think about.
Bologna? Florence? The Dolomites? Trieste? So many possibilities! Have fun!!!