For the occasion, the state museums in Florence and surroundings will be offering free entrance!
Several of these are already normally free so if you wish to optimize your itinerary in Florence, you can visit them on a separate day. These include the various Last Suppers, the Cloister of the Scalzo, the Corsini Villa of Castello and the Hall of Perugino.
EDIT TO ADD March 6, 2012: The Palazzo Vecchio Museum as well as Cappella Brancacci will also be offering free entry for women. Palazzo Vecchio hours for Thursdays are 9am-2pm, the cappella Brancacci (piazza del Carmine 14) can be visited between 10am and 5pm.