One day is not enough for both the museums and the hill towns. You need a full day for each.
The amount of time you spend in the museums depends on your personal love of art. Personally I don't believe in spending more than 2 or 3 hours in any museum. Accademia is small and one hour would be enough for me. Uffizi is significantly bigger.
All rental car agencies near the station are located on a street called Borgo Ognissanti, about 5 minutes walk from the station. There is no chance of getting a ticket while exiting that area. To return the car, the agency will tell you the itinerary to follow to avoid fines. In any case cars are allowed to enter the ZTL to take the car to a garage or rental agency. The garage or rental agency will then communicate the license plate to the City website so that no fine is issued even in the event your car gets photographed while entering the ZTL. What you hear in this forum about the ZTL is mostly mythology. I lived there most of my life and visit at least once a year, yet I got no tickets since the ZTL was created in the 1980's.