In Padua there’s a volunteer group that offers English language tours of the interior of the amazing astronomical clock tower. They’re limited to 6 or 8 people max (I think) and only available 2 days a week—we went on a Saturday prior to the start of our VI tour this May. You pay a donation at the end of the tour. We thought it was fantastic. I think you can’t book with them until closer to a month or two in advance—this is not well known (I wouldn't have known about it at all had someone else on the Forum not mentioned it).
Almost anything else you want to do on the tour does not require pre booking or can be booked a day in advance, once your guide has shared the schedule for the next day (which could change from the proposed itinerary— our guide made some changes so that we saw a couple of things late in the day when crowds were minimal). We really enjoyed the Orvieto Underground Tour and the Puccini concert in Lucca. We booked each of these one day ahead.
I would suggest you do some restaurant research and book one or two places ahead. We had the best meal we’ve had anywhere in Italy at the tiny Osteria da Pasquale in Lucca. We had made a reservation by phone weeks ahead; when we arrived there was a hand written sign on the door saying they were completely full for the evening so we definitely wouldn’t have gotten in otherwise. (If you go, get there hungry, ask your server for suggestions in ordering, and take those suggestions— OMG, so good!). In Montefaco I’d recommend making a reservation in advance at Enoteca L’Alchimista— our second best meal of the trip. We found overall that there was a huge difference in the quality of the meal/value for the price when we either researched and booked ahead OR took the advice of our guide. The very few lousy overpriced meals we had on the trip were at places where we had done neither.
Our guide offered an optional late afternoon trip to Civita (from Orvieto) which for me was one of the wow moments of the tour. You might ask your guide one day one of the tour whether they plan something like this; if not maybe the guide can help you and some of your tour mates arrange transportation to go there on your own, either very early or late in the day to avoid crowds.
