Island of Elba

I know you are looking for personal recs, but here are some good resources in the meantime. (I have done a little digging but ultimately I decided to stay on the adjacent mainland):
https://www.visittuscany.com/en/towns-and-villages/elba-island/
https://www.visitelba.com/
https://italysegreta.com/a-love-letter-to-lisola-delba/
https://visitelba.info/en/
https://www.italia.it/en/tuscany/things-to-do/the-island-of-elba-and-its-history
I'd plan to pick up a car on arrival, but that might depend on how much time you will have (I'd want at least three full days to make the travel worthwhile).
PS Hope it is okay to say that there is a regular on Trip Advisor forum from Elba, so if you have specific qs you do not get answers to, I would try there as well.

A car will be useful for the Dolomites and Tuscany, including for visiting Elba. It will be useless and a nuisance to have in Florence and any other big city you plan to stay in (like Venice or Rome). Plan an itinerary which leaves the big cities at the beginning and/or end of your itinerary so that you can limit your car rental to the time between cities (mountains and countryside) where you will use a car. A reservation may be necessary for the car ferry from Piombino to Portoferraio (Elba) if you travel on weekends. If not, it is probably still advisable to do so, especially if you go in September.

If you decide to not stay in Florence proper but instead stay out in the country and use the car to visit places, Rick’s guide book mentions a great parking solution for Florence. There’s a big parking lot right off the A1 motorway, with its own exit (one exit south of the highway to Pisa and Livorno). It’s not very expensive and Tram 1 starts/ends there. The tram ride is about 25 minutes and you see the part of town where regular people live. We used it twice when we were there last month and it worked out great! Good luck!