Ben, I think you are on the right track. You will be both a traveler and a tourist, and hopefully will not be obnoxious at either. It is important to visit the places and sites that are the most important to you, and it is also important to take the time to smell the roses, taste the foods and enjoy getting to know some Italian people. So, don't even try to program every part of every day.
You don't indicate what season you will be traveling. High season, roughly May through September will be crowded with visitors in the most popular areas, and will often be very hot, especially in the late mornings and afternoons in the summer. During those months, it is probably more important to map out your trip and book rooms in advance. Also, plan some down time during the afternoons, ideally in your room, but at least in a shady park. In the off season months, you will have more flexibility if you choose to not lock in lodging in advance, you likely will not have such heat, but you will have shorter daylight hours and.likely some rain.
You also don't indicate the particular interests of you and your traveling partner, whether those include history, art, being outside in nature, cuisine and wine, photography, shopping, etc. etc. if you give us a better idea, many here on the forum could share their own top "must see or do" sites.
Italy is wonderful, you really can't go wrong, as long as you avoid some of the pitfalls. Do not travel with many or large bags that turn every travel day into drudgery. Follow basic safety guidance, so no one takes your passport, credit/debit cards, stash of cash, or valuable electronics. And, don't program your time so much that you return exhausted with bunches of photos but no real memories or experiences or passion to return again and again!