Three full days in Rome was enough for us. Vatican (recommend a private tour) and the rest of the city can be covered in that time. We stayed about 2 blocks from the Trevi Fountain which was nice.
For us, we preferred our 7 days outside of Florence (rented a villa) and get a car. Florence is fantastic especially if you like museums/art and is a great launching point by car for Lucca, Pisa, Siena, San Gimignano, etc.
If we did it again, I would have started with Rome then Florence. We did in reverse order and wished we would have had the time to "relax" more in Florence vs. the quick pace of Rome. YMMV