Solo, Fiesole works.
What Fiesole actually feels like, beyond 'hilltop escape': it's where wealthy Florentines and the English colony (the Brownings, later Bernard Berenson at nearby I Tatti) decamped for the cool air, and that languid villa-and-cypress calm still hangs over it. Climb the few minutes up to the Monastery of San Francesco at dusk and the whole Arno valley lays out below with Florence's dome floating in the haze and the cicadas going — it's the panorama the city can't give you of itself. The Roman theatre still hosts summer concerts. The honest catch: it's a modest town, not a major sight, and on a tight first trip the in-town masterpieces win.