If you are not that keen on art and want to avoid the crowded rooms of the Uffizzi, then cross the Ponte Vecchio, walk through Santo Spirito to the Palazzo Pitti and the Boboli Gardens, You can see some lovely architecture and several different collections (not just paintings) in the Palazzo without it being overwhelming. The Boboli Gardens are wonderful - a lovely oasis in central Florence.

To escape the heat, take one of the footpaths up to Piazzale Michelangelo or there is a bus. You can also reach Forte Belvedere by bus.

Another recommendation for Fiesole. It's a quick and easy bus trip (#7). We found the Etruscan ruins really interesting - and there is more to see. You could see most of it in a couple of hours, half a day.

Thank you everyone for your lovely advice. I was a heavy user of this forum probably 20 years ago when it was hard to get online information. It is great to see that it is still as useful as it was then.