I have not checked for July, which is high season but incidentally is also the time of the year when I go to Tuscany every single year and always rent a car for the entire period (always with AutoEurope or Kemwel, its sister website)
It is too early to check rental prices for July now. I noticed over the years that AutoEurope tends to have more contract deals within 3 months from the time of travel. In any case you should check prices also in their global site (www.AutoEurope.eu), which is geared to European customers, as prices there tend to be lower. I usually book my cars for July in May or even early June.
I can tell you that before Covid, in the month of July, I never spent more than $80/day, with very large cars. I went back to Italy after Covid in July 2022 and spent $1500 for over 2 weeks (so over $100 day) for a compact car (a Fiat500 L, a large hatchback). I doubt you will spend more than $150 a day, it is simply impossible. Check again later. For $400 you should be able to find an economy car for 3 days not one.
An alternative could also be to go to Florence and visit San Gimignano by bus while you are in Florence as it is not far.
Personally I also think that going from Cinque Terre to Pisa then San Gimignano and maybe somewhere else is too ambitious on the same day. From Cinque Terre to Pisa it is at least a two hours trek. Then you need time to drop off your luggage at the station storage facility (15 min at best) followed by at least 10-15 min to go by taxi from the station to the Piazza dei Miracoli (where Duomo, leaning tower, baptistery are). Even assuming you want just a photo pretending to hold the tower you will spend another half hour there. Then you need to go back to the station to pick up your bags and take the people mover to the Pisa airport to pick up the car. So another hour is gone, There you need to go through the wait and process for the rental car pick up, and find your way to the freeway entrance, which fortunately is near the airport. From the time you arrive at Pisa airport to the time you enter the freeway will certainly take another 30 min at best. By now it is probably way past midday and already tired by the busy morning activities and travel and you are still in Pisa. Now you are on your way to your next destination. Assuming your first destination is San Gimignano, it is a 1,5 drive plus time to park outside of the walls and walk inside to see the town. 2 more hours are gone. Add another hour or more to see the bare minimum, then you need to get back to the car. Potentially you could have gone first from Pisa to Volterra (one hour drive), visit Volterra, then go to San Gimignano (45 min drive). The drive from San Gimignano back to Florence is over one hour. To all these time estimates you need to add the time to get lost and maybe pit stops for bio breaks (including some food).
So no matter how you look at it, it is going a very busy day with very little time devoted to the driving tour (basically afternoon only). If you want to see Pisa, take your time there, and forget the basically half day car rental, then head to Florence. Then if you stay in Florence a few days you can visit San Gimignano by bus from Florence or even rent a car while in Florence for a truly full day.