True of the museums and palazzi, but Florence is like an outdoor museum so a lot of it is just walking around and going into random of the many, many churches there. You'll find paintings on the walls that have been there since the renaissance.
The duomo/cathedral itself is free to enter, but there's not much in there anymore. If you want to climb to the top it's a separate entrance and ticket, though it also gets you into the Campanile (tower beside it) and the baptistry in front, at least.
If there happens to be a huge line into the Uffizi (unlikely in Feb), go into the entrance to "book tickets in advance" and book them for the next slot (e.g. in 45 minutes). Hopefully not too many people have caught on to this trick...