LOL. My first time in Florence more tha 30 years ago as poor backpacking university student on $20/day budget, i could not afford ticket to see the real David. Finally saw it last year. As suggested above, book directly with official site www.b-ticket.com for cheapest ticket price €8 + €4 reservation fee. We did not pre-book because we had an uncertain schedule on the day of arrival and lined up for a very reasonable block and a half 30 minute wait line-up. The Accademia is not very large and probably 50% of the tourists go in take a couple photos of the David and then leave.
The Piazza della Signoria is probably my favourite piazza in Italy. Probably because 30 years ago, i spent at least an hour admiring the replica David before somebody told me where the real one was. Lots of other beautiful sculptures, nice buildings and fountain in the piazza. Great place to people watch and to eat gelato. The Uffizi is next door with great paintings, but if you are not into art, bypassing it will free up a ton of time for other things. But if you do want to tour the Uffizi, pre-book your tickets because this is a really busy one.
The Duomo is famous and is free to enter. If you buy the €15 ticket, you can see 6 related attractions including climbing to top of the Duomo or the Bell Tower (we did both, I suggest to do one or the other to save on waiting and climbing for more or less the same view. Pick the shortest lineup, usually the tower). You can also see the crypt, cathdral, museum and the baptisry on the same ticket.
There are other churches, piazzas and of course the bridges to see. There are street markets. Florence is known for its pricey leather, Santa Croce and Lorenzo Street (near a very modern Cental Market; labels say "made in florence" but i bet that is where the label was made). Lots of crypts if you are into famous dead guys. Cross the river and see the palace or go up the hill to see the view of the city. Google "Medici" and you will have planty of things to see. More than enough to fill all four days, but selected major sites are doable in a day, if you are doing Siena and a "Tuscany tour" on the other days and are in a rush.
I actually find Florence more enjoyable than Rome. So much to see and experience in a very short walkable area. Everything in Rome is just bigger and more spread out. In Rome, you need to know how to take a taxi, Metro or bus in the city. In Florence, i have no idea because i have never had a need.
One little known free attraction about one block from the train station: Officina Profumo-Farmaceutica di Santa Maria Novella. Google it.