You do know that a big part of Florence, is what's inside those museums?
At the very least, take a guided tour of the Uffizi, the guide can provide insight into WHY certain paintings are significant, WHY this particular work of art is a big deal. A guide can provide perspective...you know, that concept that was a big part of the Renaissance and how it changed things. The Uffizi should take 1-2 hrs total, depending on what you choose. I think a big part of what people miss out is, how much of what humanity learned/developed was lost during the medieval period. Cement had to be relearned, humans had to relearn how to build a dome, statues and painting were crude and almost elementary until the Renaissance. From the end of the Roman period to the 1400's the Renaissance brought that back, nearly 900+ years of lost technology and skill, was re-established.
If this is your first time, stay in Florence, it's much easier and you're not living out of your suitcase. Allocate a day and take the bus/train to Siena. Siena is very high on everyone's must visit list and is a nice complement to it's rival Florence, eat a meal or, two there. Pisa I would skip, if you have to get that funny picture of the leaning bell tower, do it and leave. It ranks amongst the most overrated tourist destinations. Instead, visit Lucca, the medieval walled city that for a time rivaled Florence and Pisa. Small and compact but, lots of interesting nooks and crannies, rent a bike and ride along the top of the wall or, wander the narrow streets. It's food is also a bit different than Florence as well, ask the restaurant about the local specialties. Arrange a wine tour on another day, spend the day or, half a day with a guide and they'll take you to several wineries, have somebody else do the driving while both of you enjoy the views.