For one of our classes we went up the hill past Piazzale Michelangelo and explored the churches there. At San Miniato the monks make and sell honey and various other products in a small gift shop.
My favorite part though, was the graveyard. The graveyard there is massive and so different from American graveyards. Not only does it seem to go on forever, but the graves are packed very closely together, and they aren’t located on rolling green hills. Some of the statues and houses were truly amazing, and it was interesting to see graves from pre-unification (in case you didn’t know, Italy did not become a country until 1861) and WW1. There were also many graves with pictures of the deceased on them. We spent quite a while wandering through them and admiring the artwork.
San Salvatore al Monte was a bit smaller and less grand, but still worth a look.