June is a great time to visit Goa if you enjoy the rains. The unpleasant heat of the summer is gone, its green everywhere because of the rain, but the rain is not as severe as July as it's the beginning of the monsoon.
You can visit goa during any time of the calender. Goa has its own beauty. Although depends on your nature of traveling whether you like more crowd or not. Year end is the best time to explore more with carnival in goa. Monsoon is almost about to hit goa in june. June is very humid.
It's not a good idea to explore Goa in summers, but a really excellent idea to only chill in Goa in June.. Try chilling at any hostels for relaxed and party vibes i house. We can suggest some places in case.