All four of those cities are must sees. Unfortunately, you are on a short vacation and you only have time for one or two, or else you're going to ruin your trip.

Going from city to city and not staying in one place so that you can experience it rather than, "do it," as in, "I've been there, I have the picture of me holding up the Leaning Tower of Pisa to prove it," is to visit Italy like a tourist, where you don't really gain much. Visiting Italy is not about how many cities you can squeeze in. It's about experiencing a completely different lifestyle. Italian culture is very different from American culture, and is also very different from Italian-American culture. You can't experience it on a train. Get to know it, and it will rub off and enrich you.

Even in ten days you don't have time for more than two cities. In your shoes with ten days I'd fly into Venice, then take the train to Rome and fly out of there. Just split the ten days between those two. If you are only going for a week then just Venice, with a side trip to Verona or Padua, or even other cities that I could suggest. On the plus side, you are going at one of the best times of the year. A week in Italy in April is better than two weeks in August.