I need more information to give my opinion.
- Number of passengers
- Exact address. Near Fiesole is too vague.
- Day of the week and approximate time of arrival of your flight.
With the above information I can give you the estimated cost of a taxi.
A taxi from the airport to Fiesole should not cost you more than 35€. However one taxi can carry only 3 or 4 passengers (there is a supplement of 1€ per passenger for the 4th passenger and up).
You say you are staying near Fiesole. Whenever an American says "near" I get worried. I had a girlfriend in Florence in my young days who told me she was from 'near' San Francisco. It turned out to be Mendocino, which is a close to San Francisco as Switzerland is to Florence.
If your villa happens to be in the countryside, and not walking distance from Piazza Mino da Fiesole (which is the main piazza in Fiesole) a rental car is likely an absolute must, in spite of the terrorist advice you received above from Lee. Fiesole is nowhere near the ZTL of Florence and the likelihood of getting inside the ZTL by mistake going from the airport to Fiesole is equivalent of the likelihood of ending up by mistake in downtown Philly, on the way from NYC to Doylestown.