Wayne, This is a totally biased opinion below.
Italy is primary a North and South country. The North is more European and vibrant. The south is more impoverished, flat and dirty. Northern Italians are not as friendly the Southern Italians and the Northern Italians are not nearly as friendly as the Austrians to the north, but don't let that deter you from focusing on the north. They have a good reason to be so proud. I would consider Rome and Pompeii (Both need seeing) on the Southern side and I would not make Rome my main home.
(Nothing is really kid friendly here, but if you are determined I say go for it, we toured Greece with a 7 and 4 year old -it was a lot of work.)
I agree on focusing on Tuscany. I spent 1/2 year in Florence while studying at the British Institute. I never got tired of Florence. Opera, Art, History, gardens, great food, great open market shopping, Ponte Vecchio, and everything in walking distance. Never missed an opportunity for a real gelato (try several samples).
If you make Florence your main home, Pisa is an hour train ride west near the cost (nice day trip- nice football stadium), Sienna and Assisi are also good Florentine day trips. I loved San Gimignano I would make that a return day visit (nice white wines). Fiesole (hill to the East) is close and good for an evening Dinner and day views of Florence. Per our Art professor, one little known Gem is the country home and gardens (north) where Botticelli painted the La Primavera (Uffizi). We had a picnic there with some of the British girls, no one was in sight. You will have to do some research on bus numbers because it is not on the tourist map. It is on the north side of town and not an area worth seeing otherwise.
In Florence, the Duomo is best seen from the top of the bell tower, but you should climb to the top of the Duomo as the climb is a feat in engineering worth while. Apart from the Uffizi, much of the art worth seeing is in the chapels (Michaelangelo's David) and cathedrals. The Church Santa Croce has some of the more important figures buried there.
Venice is an overnighter, but you can hit Modena on the way and tour the Ferrari factory. It was closed when we went there, so you may want to get a open hours schedule (BTW There is nothing else there). You can see Venice in one - two days (more touristy).
Rome is an overnighter, you could spend a week there easy, Vatican, Coliseum, but it is a big city and not pedestrian like Florence. Might as well see Pompeii while your down there.
I agree on the smoking thing, If I were to go back for several weeks, I'd temporarily pick up smoking just to enjoy myself better. When in Rome...
