Day trips from Florence?

If you mean 4 nights and 3 full days, some (including me) would probably want to stay in Florence on a first trip to Florence-- there's that much to see and do, so give yourself time to enjoy it. Some travelers will feel differently about this.
Some newer travel try for Pisa, some even try for the Cinque Terre (definitely don't recommend CT as a day trip in your situation)--but the question is whether the time and effort it takes to do either one of those is worth the time away from Florence, if you actually have less than 3 full days in Florence.. If you had 4 full days in Florence, maybe.
[edit after seeing 2nd post] Lucca deserves most of a day, but is memorable and not as frantic as Pisa.
What's your mode of transportation?

Lucca - beautiful little place. About an hour and 15 minutes from Florence and a world away from the heat and crowds.

Thank you. I will check it out. As well as enjoy Florence.

Siena is definitely worth a look. It's about 90 minutes by frequent train or bus from Florence. The Piazza is fun to hang out in, the Palazzo Pubblico and Museo Civico has an interesting collection of art, including the allegorical cycle of Good and Bad Government, and the Duomo is very large. The tower on the piazza gives a great view of the Tuscan countryside.

RS has a lot of material on Siena in the Explore section. His opening description is very accurate.

Situated atop three hills, Siena qualifies as Italy's ultimate "hill town." Its thriving historic center, with red-brick lanes cascading every which way, offers Italy's best medieval city experience. For those who dream of a Fiat-free Italy, Siena is a haven. Pedestrians rule in the old center of town, as the only drivers allowed are residents and cabbies. Sit at a café on the main square. Wander narrow streets lined with colorful flags and studded with iron rings to tether horses. While nearby Florence has the blockbuster museums, Siena has an easy-to-enjoy soul: Courtyards sport flower-decked wells, alleys dead-end at rooftop views, and the sky is a rich blue dome.

We have been to Florence twice in the last 2 years. 1st trip was only 3 days and last year we rented an apt for a month and took day trips to outlying cities. With only 4 days I would make Florence your home base and take day trips to wherever you want. Train and bus service is fantastic and fast. You could easily spend 4 days just in Florence to see the sites. Without knowing your interests it is hard to recommend an itinerary. If you want good places to see outside Florence consider; Siena, Lucca, Bologna, Tuscany wine cities and Pisa (I've listed these cities/places in my personal preference of places to see).