I think the best time when you should go there is spring, because the weather is very good, but is't not too hot, so it's great.
Piazza
dei Miracoli is really well worth visiting, it's one on the most
important places in the world: there you can see the leaning tower, the
baptistery, the "Campo Santo" and the Duomo Church.
Make sure you go shopping in Corso Italia, the main street, full of beautiful shops.
Another nice thing is to go for a walk along the "Arno" river, the main river in Tuscany.
If
you have a time, don't miss the ice cream parlours in the Lungarno, the ice
cream is well wort trying! If you love reading, don't miss the parks, especially the Giardino Scotto, where you can relax, read and watch the world go by.
Martina Fedele