Florence offers plenty of free activities to keep you occupied during your stay. You'll find much to do just by taking a look into what's available and which sights are free for you to enter. Exploring the city doesn't mean that it has to cost a lot of money, and with a little research, you can enjoy your time in Florence and make memories--free of charge.
Consider climbing up to the steps of San Miniato al Monte for a wonderful view of the city and a chance to see a working monastery. It's a truly magical experience catching mass, and you can enjoy the sounds of chanting monks while you peruse the church and admire its beauty. You can also take home a little souvenir from the monks here if you would like.
No trip to Florence would be complete without making sure to walk across the Ponte Vecchio. It's one of Florence' most iconic sights and is only a short walk away from the rest of the major attractions in the city center. While you're in the area, you'll want to visit Piazza della Signoria for some people watching and a scoop or two of some of the city's best gelato.