Hello Mr. Asmera,
Ooh, your trip sounds great! I've been to Italy several times and I can assure that it's one of the best places to visit.
4 days in Rome should be fine.
2 days in Venice are also good, as it's very small and so may days could bore you.
All the Toscana region is also a pretty one to visit, with Pisa, Firenze (if you are an architecture student, you'll love it!), Verona, Siena (lovely!).
Just let me show you the travel guides I've written about some places in Italy, specially Venice and Rome, maybe they'll help you plan your trip: -snip-
Regards and bon voyage!
[ Edit: Please use the personal messaging function ]
I think that you forgot the city of the most important italian people, famous in all the world for his engineer, painting, scienze studies...
Leonardo da Vinci was born in Vinci, and in Vinci there is his mouseum and his house.
for find accomodation and useful information.
Visit italy with no visit Vinci is bad...
you can skip Pompei and go to Ostia Antica instead. It's 30 minutes outside of Rome and you get pretty much the same thing. And it's really close to the beach, too. Pompei is about 3 hours away from Rome. If you're going to Sorrento or anywhere on the Amalfi coast go ahead and hit up Pompei, otherwise skip it and spend more time in Rome.