Restaurant recommendations for families in Florence, Rome?
If your two boys are good eaters, and well behaved, then you'll pretty much be welcome anywhere you go. There are many threads on this site, for both Rome and Florence, that list all of our current picks. I would say that any but the very expensive/high end places will be perfect for you.
One thing I'd add, is with two boys in tow, that you may want to do a bit of extra research for gelato and pizza stops, in addition to restaurants. And by pizza I mean snack type pizza by the slice. There's nothing that gets a 7 or 9 year old in the right frame of mind for visiting another museum or church than the promise of ice cream or pizza at the end!
Hope this helps!