June is one of the hotter months. So I would advise you to leave the beaches and go to the hills to enjoy. Hit the beaches during the winter months typically from November to maybe mid feb. However, if you are still intent on going to a beach, then LAKSHADWEEP. Its an undiscovered underrated paradise. Besides you have to undertake a sea voyage of 14-18 hours depending on the island you are staying in and it starts from Kochi. The entire experience will be quite unlike anything you have experienced before.
If it’s about these 2 then, Give a shot to Andaman islands.
Try scuba diving or snorkelling.
Stroll around beaches in different islands and explore the hidden beauty, can dive into some kala pani history also.
Both the options are not suitable for June as it is the beginning of monsoon season. Rains in Andaman are bad and you may end up spending most of the time indoors only. During monsoon the sea throws away the trash back to the shore and hence Goa beaches aren't the best to visit during that time. You can try visiting Ladakh or Spiti Valley instead.
if you have never been to South i suggest this route. Cochin- Athirapilly waterfalls- Valparai- Ooty- Masinagudi- Muthumala National Park- Gundalpet- Bandipur National Park- Coorg- Mysore. Advantage post monsoon waterfalls will be full, lush green forest and less crowd