In June, the flow of tourists in Italy begins to increase intensively. You won't be able to lounge on the beach as you did in May. You will not be able to enjoy the sights in silence as in April. Be prepared for the fact that everywhere in the tourist spots you will be followed by crowds of hungry for experience and entertainment.
But a holiday in Italy in June is an undeniable advantage — it's the perfect month for a beach holiday. The air and water warm up to the optimum temperature (in May with this may still be a problem, and in July is often too hot).