We will be staying 3 nights and will have a rental car. Our apartment does not offer a parking spot, so will need to find parking lot/space. What options will we find in Fiesole? We plan a couple of day trips via car, so will need access to the car.
My first suggestions is to have the apartment owners point out good parking spots around the area closest to them - they should know when there is street cleaning or the safer areas.
Whenever I go to Fiesole for concerts in the summer I find parking behind the Roman amphitheater - and along via delle Mure Etrusche (it was free up until last year) but you need to check, every year it can change.