Rental Car

There is probably better car selection in Florence. But if you can find a car which you like in Livorno then rent it in Livorno.

You can do either. I'm sure there are offices in Livorno. If not Pisa airport is next to Livorno.
However renting in Florence might be more convenient because you save yourself a trip on a train (where you have to haul your luggage) and the taxi transfer from the station to the rental office (neither Pisa or Livorno have rental offices near the station). From Florence to Livorno is just over one hour drive, and if you pick up your rental car at the Hertz office on Via Del Sansovino in Florence, you are practically already at the entrance of the freeway to Livorno.

Linda,

Don't forget that each driver listed on the rental form must have the compulsory International Driver's Permit, which is used in conjunction with your home D.L. (so you must carry both). These are valid for one year, and easily obtained at any CAA/AAA office (two Passport-sized photos required, which may be provided by the issuing office).

You may also want to have a look at some of the posts on the forum concerning the dreaded Zona Traffico Limitato (limited traffic) areas that are becoming increasingly prevalent in many Italian towns & cities (especially Florence!). Some of these are enforced by automated cameras and some by local police. Each pass through one of the automated Cameras will result in a €100+ ticket and visitors often don’t know of these violations until several months after they’ve returned home.

Although I bought an international driver's license this year I have never bought one before [5 trips] and had no issue.

Yes you need to watch for ZTLs but the car rental place in Florence is at the airport far from the city center.

Rent the car at the Florence Airport which is right on the freeway that brings you to Livorno.