For your first time in Italy, then definitely do Rome! How long will you have, and what time of year?
I've not been to Milan, but have been to many other parts of Italy, and the only place I probably wouldn't return (and not because it weasn't nice, just didn't have tonnes to do besides wine!) was the Asti region.
I'd definitely recommend:
Bologna (the region Bologna is in is renowned in the whole of Italy for its food, I've always eaten very well here, and would happily return again and again - I've been 3 times)
Venice
Tuscany (the countryside, Florence, Siena, Lucca, Pisa - just for a few hours, Montepulciano...)
Umbria - Perugia, Assissi, countryside
Amalfi Coast - also take in Pompeii (and Herculaneum) while there
I've never had a bad time in Italy.