That's easy enough anywhere in Italy ;-)

If I take people figuratively here, should I give figurative advice?
Spread your wings and soar!
Hope that's helpful.
Then go to Le Marche or Puglia or Umbria or Lombardia. Why waste your time in all the museum-heavy tourist icon spots? You can enjoy all those very general things you mention in any corner of Italy.
If you don't want to spend time on things related to art (which I'm presuming includes architecture), I'm not sure I understand why you're going to Florence at all. The usual advice on this forum is that there's no such thing as a must-see, but I would say that all the main tourist sites in Florence are related to either art or architecture. You can walk along the river bank, and to the top of the hill to see the view, I suppose. But if you don't want to see buildings, pick somewhere else, seriously.
Yes, there are a number of easy day-trip options from Florence.
If you're not sure what there is to see on the Amalfi Coast, why are you going? (A genuine question.) You must have some idea of what you want to see there. But read guidebooks and do Internet searches for lots of suggestions.
A day trip to Capri is worth it if you want to see the things that Capri has to offer. I imagine there would be no need to book boat tickets this far in advance, perhaps a day or two before you want to travel, to be on the safe side, but May is not peak season.
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