You won't get much of the Italian culture by traveling al the time Choose one place--my choice would be Rome but Venice or the lakes would be lovely too. Go there and stay in a smaller hotel. Sit in the piazzas and drink coffee or wine. Watch life. Go to a trattoria fro dinner, not a fancy restaurant, but one where little english is spoken. Struggle through ordering . Laugh at yourself. Make friends. Listen to music.
The culture of many european places is based on a slower mode of life than our American go-there-and- see-everything lifestyle. You will enjoy it!