I think your itinerary looks good but will add one thought about leaving Milan out. As it is your first time in Europe, I think Milan is an excellent place to dip your toes rather than jumping right into Rome which can be daunting to tourists. Given that Expo Milano 2015 begins on May 1, Milan will really be putting its best foot forward. In addition to seeing the Duomo, you will have the opportunity to sample delicious Milanese food in the Brera district.

Having visited 35 cities in 16 countries, I always recommend foreign travel as a stepped approach where you build your travel skills in baby steps to avoid pitfalls and maximize your opportunity for enjoyment; Rome is at least step 2 if not 3. For sure, Rome is awe-inspiring but can be a challenge for even seasoned travelers. I would hate to see such a wonderful trip be anything less than wonderful.