"the copy looks exactly the same as the original."
Unless they've gotten a different and much better copy since 1989 (when I was last in Florence and saw them both), this is absolutely NOT TRUE. The David you can see for free looks nothing like the one in the Accademia. Having read differing opinions (some books said what Roberto said, others disagreed), I was quite startled to see just how different, and how much better, the real thing looked compared to the copy.
I know Roberto is a native Florentine. Since I've been to Florence exactly once in my life, 25 years ago, normally I would never contradict him. But this is one case where I must make an exception. (sorry, Roberto).
As for the rest of your question, the answer to "how should I spend one day in Florence?" is the same as "how should I spend one day in New York?" You will have to be ruthlessly selective, looking at lists of "highlights" and choosing as many of your own personal "must sees" as you can squeeze into your time. Uffizi vs. Accademia vs both vs neither? Only you can make that call; read about them and decide.