We just took a cruise April 26-May 10 it went from Miami to Civitavecchia (Rome). We took the train to Venice Italy. The weather was very nice spring weather not to hot not to cold. I had hear Venice can be smelly in summer because of the heat it didn't smells at all when we where there on May 12-14.
I suggest you go in Spring, the weather is good and the sailing is smooth.
If you end in Civitavecchia (Rome), I also suggest you hop on a train to Venice it's only about 55 euros per person for a standard 2nd class ticket and well worth the trip on a Eurostar train it's about 4 hours.