Where will you be coming from for the day trip?
I highly recommend the Walks of Italy walking tour of Florence. You meet at 8:30 at the Piazza San Marco, check in and then the tour walks a block or so to the Accademia, arriving just as they open. Your tickets are provided and you walk right in. You then spend an hour at the Accademia, which was plenty of time. By the end of the hour it was getting crowded and when we left, there was a long line to enter. There were only 10 of us on our tour. I think they limit it to 12.
From there, you walk to the Baptistery and the Duomo, then walk through the heart of the city. The tour ends at the Ponte Vecchio around noon. Marco, our tour guide, provided great suggestions for lunch.
We also signed up for the tour of the Uffizi, which started at 2:15. There were only 6 of us for this and Marco didn't even use the headsets. Again, we walked right in. The Uffizi was wonderful. There's nothing like standing in front of the Birth of Venus! We didn't finish until 6:00 and were free to stay until closing.
The problem is there was so much to see other than those two tours, which would pretty much eat up your entire day. You might consider the morning tour, which is a great overview, then selecting the things you want to do in the afternoon.
My wife and I got to see the gates of Paradise when the original panels were on the doors. That was August, 1966. On November 4, 1966, the Arno spilled over its banks and flooded Florence. The panels on the doors were dislodged. Luckily the grating around the doors trapped them and they were recovered.
It was in Florence, August 10, 1966, that my wife and I shared our first kiss.