jb,
A few thoughts on your proposed trip.....
Rather than pay the high one-way drop fee, you might find it more cost effective to use a combination of shorter car rentals, train or perhaps a budget flight. I haven't worked out all the possibilities.
If you're staying in Nice for a few days, it's easy to get to Monaco so no car is needed. I'm not sure what the post Covid situation will be like, but there used to be a Bus from the main station in Nice to Monaco. The cost was very reasonable and that would avoid any parking issues.
Your profile doesn't indicate your home location. If your home is somewhere other than the E.U., it would be a really good idea for each driver to have an International Driver's Permit, which is used in conjunction with your home D.L. IDP's are easily obtained for a small fee at any AAA / CAA office for a small fee, and these are usually valid for one year.
With only nine days to work with, it would be a lot quicker to travel by train from Nice to Rome. You'll be on Regionale trains for the first part of the trip, but once you connect with the high speed trains in Italy, it's a very fast trip with no wasted time. That's a long trip to do in one day, but you could (for example) spend one night in Milan (about 5 hours from Nice) and then take the high speed to Rome the next day (about 3 hours direct). You could also use a budget flight. If you've never travelled by train in Italy, there are also some potentially expensive caveats to be aware of on trains.
If you haven't driven in Italy before, you'll need to be vigilant to avoid the ZTL (limited traffic) zones which exist in many cities, as there are hefty fines for each pass through them. Florence is heavily covered by automated ZTL cameras so not a good idea to drive there unless you know your way around. You likely won't know about the fines until several months after you've returned home.
