There are many places of interest in Florence and its surroundings (museums, churches, palaces, monumental parks) regularly open on August 15th.
On Thursday 15 August numerous National museums will be open for the whole day: Uffizi, Medici Chapels, Palazzo Pitti and Boboli Gardens (the Academy Gallery will remain open until 9pm). Other state museums (Bargello, Archaeological museum, Palazzo Davanzati and San Marco), however, will only open in the morning. The parks and Medici villas of Petraia, Castello and Pratolino are also open all day. Among the civic museums, Palazzo Vecchio (9-14) and Forte Belvedere (10-20) are regularly accessible.
The Galileo Museum, Palazzo Medici Riccardi, Dante's House, Museum of the Innocents and Football Museum can also be visited for the whole day. However, all Natural History museums are closed, including the Specola. Most of the main churches (Santa Maria Novella, Santa Croce, San Lorenzo, San Miniato al Monte) will be open only in the afternoon, while the Cathedral of Santa Maria del Fiore will remain closed for the whole day, but guaranteeing access to the other monuments of the complex.
For all details, including opening hours, consult the museum opening hours.