crowds in rome and florence during the eight days after new year

First, it is always crowded so it is just a matter of whether it is crowded or very crowded. I am guessing - but since some of the Christmas celebration in that part of the world continues until Jan 6th, it could tend to be very crowded.

I agree, however, people think Firenze is crowded, but you have not seen crowded until you get to Rome. I was just in Rome in Novembre, incredible crowds, but i can say the most behaved polite crowds anywhere, respectful, kind, thoughtful people from all over the world make up those crowds so come join us and have a good time.

The museums will be crowded. Make reservations to avoid the lines.