I live around the corner from the Vatican Museums entrance and often walk by the "line." Even during peak season the line is usually gone by 12:30 - 1 PM. Now (October), there is usually no line after about 11 AM. Part of this does depend on which day of the week you are going - and time of the year. But if you plan to go in the afternoon, you should have no trouble getting in. When I take folks in we usually do a local market, then the Basilica, see the tombs, climb to the top of the cupola --- then go do lunch! After lunch, re-energized, we head to the Museums. In the last 50-60 times I've been in the Museums I have not waited in line - It's all about timing. For more info on the "legend of the line," read this post on Should I pre-purchase tickets for the Vatican?

Early in the AM, the tour groups assault the Vatcian and they have first priority, thus creating the backflow which becomes the line! It's also extremely crowded in the AM in the Museums because of this. The last entry into the Museums is 1600, and you will start being "herded out" around 1730, as the Museums will close ON TIME at 1800.

In Florence I've had mixed experiences. Due to time constrainsts I have booked tickets in advance - and on other trips I've just walked in. I find the lines, if there, longer at the Uffizi than the Galleria Academia - but that's only based on 10-12 trips... so I'd rely on a local for better info. Good Luck!