As one of the main attractions in Florence this is a very busy museum. We were fortunate enough to get a booking through our hotel. The building housed magistrate offices from the late 1500s. It was opened as a public museum in 1765.
The Uffizi costs Eur15 (like Gallerie dell'Accademia) and three hours is about the right amount of time to see everything. There is a lot more to see here.
Broadly speaking, you will see: Religious art, sculptures and non-religious art. Having just seen religious art at Accademia, I found the non-religious section more interesting.
Navigation is very easy as most of the art is set along three main corridors with side rooms followed by an apparently new area with all the non-religious art.
I regret not getting a guide because I could overhear a guide telling lost of interesting stories. For instance, I didn't know that Leonardo da Vinci was actually a scientist and only did 40 paintings. Of those 40 we only hold 20 today.
I tried to tag along with the group that had the guide but it was very large and hearing was tough around the fringes. It obviously would have been ultra strange for me to force my way to the front!