Rent car in La Spezia, Pisa, or Florence?

I would rent in La Spezia. All of the places you mentioned are hectic, but the rental office will direct you to the closest way to get to the freeway. We did the ride from La Spezia to Lucca in only a few hours. (You go by the Carrara marble mines which you can see from the freeway.) Then you could get to the Tuscan countryside easily.

Who told you the road in La Spezia are scary? That might be true for the narrow roads at the Cinque Terre, but not La Spezia. It's normal city streets and the rental offices are nearly all on Viale San Bartolomeo (near the port) which runs parallel to Via Carducci. Via Carducci is a large street that become the 4 lane causeway leading you to the A12 freeway. Just go from Viale San Bartolomeo to Via Carducci using one of the perpendicular streets connecting the two, turn right on Via Carducci and go straight to the freeway. Couldn't be any easier.

Thank you both! I'll rent in La Spezia.

There are a few other considerations, such as when and where you'll pick-up and where you'll drop off. This article may help: http://www.apathtolunch.com/2015/11/where-to-rent-car-from-cinque-terre-la.html

We rented next to the airport in Florence and it went well but I have no data for LaSpezia so go for it. I did want to add that you should keep in mind that many rentals in Italy are manual transmission. The other thing that we found essential was access to navigation. You can rent portable navaigation with your car or for a few $ more, a portable wifi and use google maps. None of our hotels wifi actually worked for any amount of time so we were thankful to have chosen the portable. I enjoyed driving between Florence and Orvieto so have a great time!

La Spezia would be best as the rental office is not far from the train station.
I think you are not at all thinking that the easiest to drive out of rental places in Pisa and Florence are the airports but the train does not go to either airport.

Pisa you may have to get from train station to airport which makes things harder.
If there is one closer to the train station it may within a ZTL area and likely more hectic driving than La Spieza, which also makes things harder.

Florence is the same way there are places at the airport which are easy to drive out of but it is hard to get from the train station to the airport and the ones in town close to the train station are within ZTL zones and definitely more hectic driving than La Spieza.

From the La Spezia Centrale train station to Viale San Bartolomeo, near the port, it is really not walking distance, especially with luggage, therefore you should take a taxi (it's only a couple of miles).
Avis-Budget rent a car is closer to the station, however Avis tends to be more expensive than Europcar or Hertz.
If you rent on a Sunday, the La Spezia locations may be closed. in that case Pisa airport is your next best option, since the airport locations are always open. From the Pisa Centrale station to the airport there is a short shuttle bus ride. But bu the time you go the Pisa people mover (currently under construction) from the station to the airport may be open.
For car rentals check pricing also with the following consolidators:
www.autoeurope.com
www.kemwel.com
They are part of the same company but check prices in both sites. They work primarily with Europcar, Hertz, Avis-Budget. The Europcar deals are generally cheaper if you opt for the full zero deductible insurance.
If you have never rented in Europe, be aware that most cars have manual transmission unless you specifically request automatic (which generally comes only with larger models).
You will need the International Driving Permit (IDP) to drive in Italy. It is just a translation of your home license and it can be obtained at your local AAA/CAA for $15-$20 and it takes 10 min. Although the local rental car agency in Italy may not ask you for one, since they are used to seeing US or Canadian licenses, however the Italian Motor Vehicle Code requires it and in case of accident or police stop you may have to produce it along with your license. The fine for not having an IDP starts at €400, but the biggest risk might be (although I don't know) that failure to have the IDP might invalidate your insurance coverage. We all know that insurance companies (including credit card insurance) always find creative ways to avoid reimbursing, so don't give them a chance.

Thanks to all of you for your help! I just rented a car from Auto Europe out of La Spezia and feel very good about it. I appreciate all the detail!