Florence can be easily visited in 2/3 hours without to pay
In particular, I recommend this route, which you can verify in Google Maps dragging the Pegman (the little yellow man) in the streets of Florence.
Florence Santa Maria Novella - San Lorenzo Market - Duomo - Piazzale della Signoria - Ponte Vecchio - Palazzo Pitti - Boboli Gardens. (between each of these places and the next there are 5-10 minutes of walk)
Turning back you can cross the Ponte alle Grazie, parallel to the bridge Ponte Vecchio, and walk until you reach the beautiful panoramic location of Piazzale Michelangelo.
But if you want to join in a tour and have a guide to explain things (and one you can ask questions of), then take a look at the tours offered here: www.partner.viator.com/en/13618/