Grassina has many things to offer you and are all within walking distance from the apartment:
grocery store
post office
camera and computer stores
all sorts of shopping (clothing, shoes, crafts, ceramics, household items, antiques)
gym with weight room and exercise classes
pastry and bread shops
butcher shops and fish market
fresh produce shops
Friday morning market in the square
beautiful hills perfect for early morning or after dinner walks
medical center and pharmacy
church (La Parrocchia di San Michele Arcangelo)
pizzeria and gelateria (ice cream)
cafes and tap-room
tobacconist and card shop
magazine and book store (foreign language newspapers available)
florists
convenient bus stop across the street (bus #31/32)
Outside of Grassina there are also many things available.
In Antella (1km from Grassina) there is an important hospital, the Ospedale Santa Maria Annunziata, via dell'Antella 58.
There is a famous golf course on the Via Chiantigiana going towards Greve http://www.golfugolino.it/nuovo/eng/la_storia_e.htm
There is a new cycling museum at Ponte a Ema, built for the famous cyclist, Gino Bartali, who was from this town. http://www.tuscany.org/Recreation-and-Sports/
Also at Ponte a Ema there is the town library http://www.comune.bagno-a-ripoli.fi.it/biblioteca/index.html
In and around Grassina there are several sports centers for soccer