Cinque Terre is really beautiful, but jam packed with American tourists. One of their main brands of guide books recommends it as one of the top places in Italy.
I second Lucca- olive oil is their big thing there too
Pisa is good for a day trip- have flown via Pisa many times. The Leaning Tower is even weirder when you see it in real life, it’s just in the middle of this big lawn in the town centre.
Pistoia is very pretty too. https://www.discovertuscany.com/pistoia/
Beans are their local thing in Tuscany. Lots of soups.