I would say it depends on what you want to do/see while you are there. You might check when the Easter holidays are next year -- some things might be closed during that time, but on the other hand you could run into wonderful celebrations. In my book, there is NO bad time to see Italy! The last time I was there was early May and we had great weather.
My husband and I were in Foggia, Abruzzo, Molise, Le Marches and Umbria in May (the beginning). It was warm then it was rather chilly. Either way, it was the most wonderful experience. Looking forward to going back.
Have a great trip!