definitely more than one day
When I was there it was education week so all museums were free admission to all museums. Best part was for 5euro we skipped all the lines of people waiting for free so I covered everything I wanted to in basically one day.
@ Yehoshua
1.Walk around town/Ponte Vecchio/leather market (All part of a walk)
2. Uffizi
3. Shul (and/or museum)
4. Acadamy
5. Never did science so can't say.
All depends what you want to see.