Twice I've made day trips to Fiesole, the little hilly town five miles from Florence. Five years ago, I went with my Nonna (literally "grandmother," but really the name I call my host mom from my semester in Italy) and my roommate/best friend. One month ago, I returned with my Nonna and my boyfriend.
Both times, I was captivated by the Roman Amphitheater (though I haven't had the chance to see its summer performances), its Archeological Zone (dedicated primarily to Etruscan ruins), the Convent of Saint Francis, and its views.
During your hike up to the convent, make sure to stop at the terrace to contemplate the Tuscan hills and the city of Florence. Both the Duomo and Palazzo Vecchio are easy to locate, giving you a frame of reference for the rest of the city. If it's sunny enough, you can see the Arno, as well (on cloudy days, you might have to strain).
It's a 20-minute (more or less) ride on bus 7 from Piazza San Marco in Florence (but you can also catch it at the Stazione Santa Maria Novella).