If you are willing to leave the old city center for a day, visiting this beautiful and interesting museum and park can be an idea. Museo Stibbert is really close to where I live and the walking distance is about 30 minutes from the center (I’m normally bad at recommending buses because I always walk or take my bike within the city) or take bus number 4 from the station. I’ve seen that Raffaello has spotted a few nice places in this area (check articles Gelateria de’ Medici, Il Panino Tondo and Fratelli Briganti) those are worth checking out if you decide to come to this part of the city.
Museo Stibbert is, besides being an extraordinary villa in itself, a museum with a selection of paintings, porcelain, costumes and armoury (for the Japanese collection there are only certain hours and the visit must be booked, so check the website for that). Frederick Stibbert was very fascinated with armour and gathered an impressive collection that is displayed in the museum today.
The magic garden is big and very peaceful, with its aisles, statues, pond, temples and tables to sit down and read or enjoy the quiet. If you have time and have already covered the Florence basics I highly recommend you visit this little pearl.