Florence, Siena, Gimignano, Pisa, Lucca

Take the bus from Florence to Siena- quicker and easier as it drops you up in town as opposed to down below at train station

Both Lucca and Pisa are better reached by train from Florence
Neither is a hilltown and not what one thinks of as “Tuscan countryside”
San Gimignano is a train then bus from Siena

You might be better off booking a guided tour from Siena that will get you to the typical hilltowns
ToursbyRoberto.com gets good reviews- he books up early

I would do 3 nights in Florence and 2 nights in Siena. 

San Gimignano is beautiful, but I wouldn’t go unless you can overnight there, and you don’t have the nights to do it. It’s not a good town to day trip because it gets swamped with day trippers and is just not very enjoyable during the midday hours. 

I would go to Pisa in an afternoon from Florence to see the piazza with the duomo, the tower and the baptistery. 

With just 3 days in Florence, I wouldn’t allocate any Florence time to Lucca, nothing you would see in Lucca will be better than things you would be passing on in Florence.

My other option, simply to avoid train and lodge hopping, might be to keep Florence for 3 nights, and then take a train, albeit long , to the Amalfi coast. Two reasons: it is more of an aesthetically appealing coastal town as opposed to Venice, Rome and Florence which are more architectural sites (museums, art, galleries). Not too keen on the long train ride, but I think it might be a better fit and totally different than my other locations.. The Tuscany region just seems to be a little more hectic regarding all the towns we want to see. give me your thoughts on that!

3 nights (basically 2 full days plus half day on the day of arrival) are the bare minimum to see Florence’s main must see sights (if you really plan your days to their fullest). For every day trip you take from Florence you need to add one night, therefore with 4 nights, you can take a day trip, with 5 nights you can take 2 day trips. Siena is probably one day trip. You can add a few hours at San Gimignano on the way back to Florence if you start your day early.
Lucca and Pisa can be done in one day day trip. First Lucca, which is prettier IMO, then Pisa later in the afternoon (30 min from Lucca by train). Pisa is one pony trick town and everything in in one Piazza (Piazza del Duomo, aka Piazza dei Miracoli), where you can see leaning tower, duomo, baptistery and maybe the cemetery (Campo Santo). Trains back to Florence run until late (last train at 10:23pm from Pisa Centrale). Changing hotels and transferring to Siena requires time, basically almost one full day is gone with the transfer (pack, checkout, go to station with luggage, travel to new hotel, check in hotel, unpack), and to me it is not worthwhile to move just 40-50 miles unless you have more nights available.

Tuscany is definitely easier with a car
As far as AC depends when and where you want to stay/see
The area is jammed with tourists and transportation is chaotic and often unreliable-there is really no off season anymore and ferries don’t run til April

Could you post again when this trip is what your full itinerary is? How many nights actually in Italy?
Departure flight from where?

aesthetically appealing coastal town

I wouldn’t go to the Amalfi Coast from Florence. I mean, that would take most of a day.

How about Cinque Terre instead? The Cinque Terre towns are aesthetically appealing coastal towns and only about 3 hours from Florence.

hey hey frances.hess
when are you planning this trip and how many people, where are you flying from what airport to fly home to? as i count it's 10 days, which is too short of time to see what you're hoping for.
2 nights is one day, 3 nights 2 days, check-in is 3-4pm and check-out is 10-11am. italy is always crowded, no off season, with the areas you want to see.
look at how many posts list the same area as you with wanting to cram it all in a round hole with a square peg. you don't want to be spending more time in train travel, looking at countrysides out the window, enjoy relaxing and people watch in city/town.
i totally agree with marco about san gimignano. we did a private tour through some places in "tuscany", got there and was packed like sardine with 8-10 tour buses, smaller tour vans, private rental cars and taxis. couldn't walk anywhere, stop in some shops with long long lines to pay with one person ringing up, gelato shop was out the door, down the front of building along back side of shop with grumpy/ill-mannered/pushy people. go somewhere else away from crowds.
wouldn't waste my time going to almalfi coast with the crowds, transportation issues as the roads are not the best in shape, hours one way from florence. go back and check your places/towns you really want see & do, come back for more ideas & help with from the posters here. want you to enjoy and have fun
aloha

Amalfi coast is at least 5-6 hours away (by train+bus or boat) from Florence (4hours to Salerno by train, then bus or boat).
So not doable as a day trip.

Cinque Terre is at least 3 hours away (by train) from Florence.
Doable as a day trip but kind of a long day for a short time at the destination.

If you have extra nights available, then it's another story.