Florence lives off tourism and this being the case there are very few places where you can go in for free. 

It is a good idea before you go to make a list of all the museums, churches and galleries you want to visit and check the opening times and prices of tickets on their Internet pages. In many cases the prices on the web may not be accurate and you will realize at the ticket office that prices have magically gone up.

For example on the Uffizi Gallery page (http://www.uffizi.com/timetable-servi...) it says that the ticket is 6.50 euros and the reservation is 4 euros, this was true in March 2009 but apparently if you had not booked by telephone and had gone to the ticket office in September 08 you would have seen that the price of the ticket was 10 euros and the reservation was 4 euros?  Same for the Accademia (http://zipmyurl.com/STbIT). 

At the Uffizi Gallery and at the Gallery of the Accademia they try to do their best, so that you can make reservations, well ahead, for the tickets in order to avoid the eternal queues.  

I would suggest ringing the Uffizi Gallery Booking In Advance service, as agencies "pretending" to be the Uffizi charge more than 4 euros per person, pre booking fee. The entrance fee is then 6.50 euros. In 2009 total cost per person € 10.50. Tel 0039 055 294 883  (They will pre book Uffizi, Accademia & Bargello). You pay nothing at this point and are given a Number for the time slot you have chosen. To save a long wait on line, it is worth hanging on to the line that connects you to an Italian speaker and not pressing the button to be put through to an English speaker, as the operators all speak English!  Don't loose the number....

When you get to the Uffizi there are no signs as to where to collect your tickets. It can be a nightmare unless you know that those queueing to get in (eventually) are on one side of the courtyard and the ticket collection service is on the other. (March 2009 Gate 3).

Once you have spent your max 2 hours viewing and have reached the cafe on top of the Uffizi building, enter and go on to the terrace to admire the spectacular view but unless you are happy to pay over € 6 for a coffee don't sit down at the tables inside or out!