What month would you consider high season starting in for travel to italy ?
June. But that doesn't mean that hotel rates will necessarily agree,
It is not like Hawaii where there is a specific date. Different regions and properties have different high season rates. In general, June as Doug says. But you may not notice rates in May or September getting much lower, it depends.
Shoulder seasons are "high season" in Italy as well. That's Apr/May & Sep/Oct. Very attractive to individuals who have the option of traveling when crowds are down and the weather is better. I've found I got the best rates in Nov (not Dec) and again mid-Jan, Feb & Mar. The trade off is shorter days, colder weather, shorter museum opening hours. Plus is no crowds.
I really think May is now high season in Italy, Patrick. This past year we were in Italy for the whole month starting in Venice , travelling through Tuscany and Umbria , and ending in the Cinque Terre and it was very ,very crowded. We were very surprised by the crowds in Venice May 1.
Bear in mind that May 1 is a holiday and Venice is a huge destination for Italian day-trippers. But, yes, in many places May gets crowded.
We were there this past September and it was VERY crowded. I thought with kids in school it would not be. There were lots of British, Gemans, Australians, and fellow Americans. Prices were the same as the summer prices where we visited and stayed. Met lots of people who were on long weekend trips from other parts of the Europe. Australians seemed to be on their winter break.