Staying In Florence at Relais Santa Croce and doing day trips to Lucca, Pisa, etc.. Should I rent car or do the train? I heard you can't park at hotels in the main part of city.
Pisa, Lucca, Siena, Arezzo (I.e. provincial capital cities) better by train or bus (Siena take bus).
Small villages and countryside, such as Chianti hills, better by car. However your hotel is not in a car friendly location, you're in the forbidden ZTL (zona traffico limitato), only residents and hotel guests allowed (just for check in or park at hotel), but if your hotel has no parking you need to go park outside the ZTL. If you rent, rent just from morning to evening, return the car before going back to hotel.
The Train! A big winner getting to these cities. Easy, inexpensive, and multiple choices for coming and going. Having a car in Florence is expensive and very difficult. Just be sure to watch for the sudden strikes of the RR system. They don't last long, but can really mess with your plans. Your hotel can keep you informed of these possibilities.