The Auditorium of Santa Apollonia is located 5km from Florence airport (FLR), and about 85km from Pisa airport (PSA). From Florence airport there is the tramway Line 2 to Santa Maria Novella train station (less than 1 km from the Auditorium), or a short taxi ride (about 20 min). Pisa airport is regularly connected to Florence Santa Maria Novella train station by bus (see http://www.terravision.eu/florence_pisa.html for the timetable) and train (https://www.trenitalia.com).
For all information about the airport and the transfer services, please find it here:
Florence is also accessible through an excellent fast train service to and from Milan, Rome, Napoli and many other Italian main cities. Between the smaller towns there are regular trains that offer a very economical option for touring within Tuscany and the surrounding regions. (see https://www.trenitalia.com and https://www.italotreno.it italo for the timetable).
If you are traveling by car, all main cities to the North and South are accessible along the A1 motorway. To reach downtown take the exit Firenze Nord, and follow signs for Firenze Centro, Santa Maria Novella train station. If you are arriving from Pisa airport, take the Florence-Pisa-Livorno motorway (toll-free) towards Florence. Once in town, follow signs for Firenze Centro, Santa Maria Novella train station.
Please note that, as the centre of Florence is closed to private traffic, it is advisable to check with the hotels about how to reach the place and about parking facilities available in the area.