My husband and I are taking a trip to Italy to visit family this May. We have a soon to be 2 yr old and this is our first time flying with her. We have a total of 9 days--> flying into Venice Marco Polo and departing from Rome. As of now, the plan is to spend 4 days in Vicenza with family, 2 days in Florence, and 3 days in Rome. We want to see the major attractions but also want time to explore on our own. Any recommendations would be greatly appreciated.
This is a very broad question, toddler aside. I suggest you take a close look at Rick Steves' Italy Guidebook and his itinerary ideas for trips to Florence and Rome. See what appeals to you. I doubt you would enjoy the Vatican Museums with a small child, so take that off the list. In order to have time to explore on your own, do not fill the days too full. Maybe a site in the morning, a walk before or after lunch, downtime/naptime, and more exploring before/after dinner. A stroller for the little one would be a good idea.
Your toddler will be a rock star in Italy. There are websites for traveling with children, and Lonely Planet guides usually have some info.
Definitely take a stroller - preferably light-weight. I've seen toddlers in Europe with a harness and leash. That seems like a good idea for when she wants to walk around on her own, so she doesn't dart off somewhere in a crowd or into traffic.