I have to disagree with this statement:
The first few days of May are not a good time to travel in Europe as there can be strikes and you can be caught up in them and unable to get from place to place.
You cannot let the remote possibility of a strike be the deciding factor in this choice. For one thing, at least in Italy, trains do run during a strike, although there are fewer runs. For another, strikes (if they happen) tend to start on a Saturday evening and end 24 hours later on Sunday. To lessen the likelihood of being affected by a train strike, you can develop an itinerary that avoids train travel on Sunday. Or plan to have a rental car.
The weather in spring will be rainier over all, but flowers are blooming everywhere and it's just beautiful.
It is true, as Roberto noted, that there are more tourists in Rome in April than in August, if you look at the charts showing hotel occupancy by month in the link that he attached. Rome is so huge that I wouldn't let that be a factor in deciding, but April is clearly not a time when you should just show up without lodging reservations pre-arranged.