Florence - The Accademia and the Bargello are pretty small, lots of time to see everything. The Uffizi isn't much bigger. I would add the Pitti Palace and the Duomo Museum (which is in a separate building and has many absolutely wonderful works, including a Pieta by Michelangelo) and the Medici Chapels for the amazing room by Michelangelo. I was disappointed by the Palazzo Vecchio sculptures - they are oddly lit making it hard to see them.
Rome - if you appreciate ancient sculpture/mosaics/frescos add the Capitoline Museum and the Museo Nazionale Romano (Massimo & Altemps). The San Luigi dei Francesi church has 3 wonderful Caravaggios. The church is French, so quite different from the other churches you will see in Italy.
Vatican Museums. OMG spend 3 days . Then there's St. Peter's . . . :-) Don't miss the Laocoon Group (there's usually a crowd around it) which was discovered during Michelangelo's life and influenced him. No words - you just have to see it.
Before I went, I read "The Agony and the Ecstasy" by Irving Stone. It will give you great insights into the processes (sculpture, fresco) and the influences on Michelangelo. Most of his extant works are in either Florence or Rome. Enjoy!!!