Don't ask me why - I can't imagine any Italian who wants to show up for work on these days (the following are free - I think other state museums, except the Uffizi may also be open):
MUSEUMS
Museo dell'Opificio delle Pietre Dure Dec 25: 13.30 - 19.30, Jan 1: 13.30 - 19.30
Laboratori della Fortezza da Basso Dec 25: 13.30 - 19.30, Jan 1: 13.30 - 19.30
GARDENS
Giardino delle ex Scuderie Reali Dec 25: 09.30 - 15.30, Jan 1: 09.30 - 15.30
Parco di Villa il Ventaglio Dec 25: 09.30 - 15.30, Jan 1: 09.30 - 15.30
Parco e giardino della Villa medicea di Castello Dec 25: 13.30 - 19.30
VILLAS
Villa Medicea di Petraia e Castello Dec 25: 09.30 - 15.30
Villa Medicea della Petraia Dec 25: 13.30 - 19.30
Full list from the Ministry of Culture.