stopping at Genoa, Pisa, and Elba en route
Take trains. They are fast, easy and get you into the town center without the hassle of finding a parking space, paying for parking, worrying about your car which may be on the outskirts, walking into the center, etc.
Are you planning to hire a car? Because if you are, I wouldn’t bother, I’d travel by train instead. Italian rail services are well organised and sensibly priced. The previous responder has comprehensively explained the complications involved with driving in towns in Italy, so I would avoid it and use the train instead if possible.
I'm not sure what your question actually is but here are a couple of points to consider:
1. Almost all Italian cities, towns and even many villages have restricted traffic zones (ZTLs), generally incorporating their historical centres. Many (the majority in cities) are monitored by CCTV and fines are automatic, taken from the card you used to rent the car (usually with admin charges added on).
ZTLs are always well-signed but generally in Italian only (obviously). Make sure you know beforehand what ZTL signs look like (just google for images). They're always placed where changing your route is possible and, if you can, find out what the ZTL limits are for each place you intend to stop.
Most hotels etc do not offer to guests visitor permits to enter ZTLs so it's best to avoid using accommodation within a ZTL unless you are happy to park outside it and use public transport, taxi or feet to get to your accomm.
Here's info (in English) about Pisa ZTL:
Sorrento: the historical centre is a ZTL, though its timings vary according to the time of year:
2. I assume you want to take the car to Elba so you'll obviously be using a ferry.
a) Check beforehand that the car rental company will allow you to take a car on a ferry. They may be ok with it, they may charge you an additional premium, they may not allow it at all ...
b) Book your ferry place in advance, and especially so if you are travelling in the busy summer months.
Ferry companies which serve Elba (some run only in the summer):
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