Buying Tickets in Advance for Florence and Rome Sights

For Florence probably the Ufizzi and the Academy.

For Rome, the Vatican Museums and Galleria Borghese.

http://mv.vatican.va/3_EN/pages/MV_Home.html

http://www.galleriaborghese.it/borghese/en/edefault.htm

You might also pre-purchase for the Colosseum (Palatine and Forum: they're all on one ticket) but if you hustle over to the Palatine first thing in morning, you could also buy the tickets there; that line will be shortest. Once you have your tickets, you can do the Palatine and Forum first and then go over to the Colosseum, or do the Coloseum first and then the other two.

http://www.coopculture.it/en/the-colosseum.cfm

Here's the booking site for the Uffizi and Accademia:

http://www.b-ticket.com/b-ticket/uffizi/default.aspx

I would HIGHLY recommend, if not insist, that you buy your Vatican tickets in advance. We avoided at least 4 hours waiting in line by just purchasing our tickets in advance on the official Vatican website. We literally walked right in!
We purchased our Colosseum tickets in advance since we did a tour, but found that you can possibly avoid some lines if you don't purchase them in advance. However, I would still recommend you buy in advance just to be safe.

For Florence, we purchased tickets to the Academia in advance, which allowed us to walk right in after standing in a short 15 minute line. We didn't purchase tickets in advance to the Uffizi and wish we would have because it was at least a 2 hour line. Needless to say, we didn't want to waste time in line so we missed out on that museum.

By all means, buy tickets in advance for the Accademia and Uffizi. We booked our tickets for the Accademia for a morning visit that, if I remember correctly, began at 11 AM. Obviously "David" is the main attraction, and is worth the visit, but we didn't spend an inordinate amount of time on the rest of the museum. We booked our tickets for the Uffizi Gallery for early afternoon. Don't remember the exact time. It is a relatively short walk from the Accademia, past the Duomo and south to the entrance of the Uffizi. We spent the rest of the afternoon in the Uffizi. You literally walk through the centuries of art in the Uffizi. With advance tickets, you avoid lines for both sights, which can be a considerable wait for the Uffizi. Really, there is no reason not to.