Ciao Vanessa,
You will both fall in love with Florence and Tuscany! If you can, I do suggest planning for more time here
I would suggest planning to mix time in Florence and visiting the city (as well as any museums you really want to visit) in with half or full day tours nearby.
For example, you can visit the Uffizi Gallery one morning and then spend the rest of the day just exploring the historical center on foot (it is very small and walkable) and just heading into what you deem interesting.
This itinerary gives you an idea of the top sights in Florence:
https://www.visitflorence.com/itiner...-florence.html
while this one gives you a few ideas on how to plan a walk around: https://www.visitflorence.com/itiner...ineraries.html (you can do the one in the main center).
On another day, you can head to Pisa in the morning (by train), then head on to Lucca for the afternoon and return by evening.
Here's a few more ideas of top day trips from Florence.
https://www.visitflorence.com/itiner...-florence.html
You don't NEED to rent a car, as you can certainly many of the top places by taking bus or train to them without worrying about car rental, parking and avoiding no-traffic zones in historical centers. If you're open to the idea of a bike tour, I highly recommend Piero and Elena from Bike in Florence (read more about what they do here: http://www.discovertuscany.com/tusca...any-tours.html )
I did a tour with them last spring between Castellina and Siena that is very doable as most of it is downhill and includes heading into Siena for a couple hours. I've heard good things of the San Gimignano tour as well. They include stops at small wineries for tour and tastings, so this is one way to include both bike + Chianti + wine ;-) You can see they have another tour with more wine stops, too!
If you want to do the wine tastings without the bike, take a look at the variety of tours offered here: http://tours.discovertuscany.com/en/...nd-Tuscany/ttd
This way you don't have to worry about DRINKING and enjoying your wine at all, while seeing the great Tuscany landscapes as well!
If you do want to look into renting a car, read this article for more info: https://www.visitflorence.com/floren...ar-rental.html
The main thing to consider is this: many cars are stick shift AND many historical centers in towns are off limits!
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