We managed to take almost all of your advice during our time in Florence, and it was very good. We found your sandwich place again and stood in a crowd of only Italian-speakers, waiting our turn. The Medici chapel was closed because it was the first Monday of the month but the Borgello (?) was lovely and uncrowded and we could take as much time as we liked. The synagogue was a great place to visit and we are so glad we went. The gelato place was jammed with Japanese tourists on Monday but when we returned on Wednesday we had it to ourselves, as well as the Academie AND the Uffizi (which we had to go to because it was right there and there were no lines at all). Jon even ate a tripe sandwich from the place you showed us and said it was tasty. I held out for a bowl of warm couscous with squash and cheese — that was delicious.
The only bit we missed was the Florentine steak but we ate delicious meals that were not quite as far away, and we can save that for next time.
In Lucca we rented bicycles and went around the top of the wall a few times before descending into the town. My cousin showed us all the medieval towers (we went back and climbed the famous one with the trees on top later) and some churches and Roman spaces — Lucca felt very familiar to us after our various walks through other towns, but much more compact and intact.
Thank you so much for introducing us to Florence and for listening closely to what seemed to be our areas of interest/curiosity. Jon says that the next time we go, you will take us through the Uffizi. I am sure there is a story behind all of those ugly old man faces on that poor little Christ child, over and over.