First piece of advice: download audioguides. Calling Florence an influential city in western history is an understatement. This is the birthplace of the renaissance. The city where bankers and artists broke with the authoritarian Roman Catholic tradition and reclaimed their Greco-Roman heritage. The arts flourished, trade bloomed, and nudity was everywhere. Walking around Florence without proper context is a missed opportunity. Download some audio tours, pop in your earbuds, and go wander.
Second piece of advice: Wake up early to line up and book tickets in advance. Florence has become a victim of the tourist hoards and much of it looks like a shopping mall. The museum crowds can make it feel like a boxing day sale where selfie sticks are half-off.