Located on the island's west coast, Cala Banyalbufar is one of the loveliest quiet beaches in Mallorca. Although it's Banyalbufar town's main beach, you'll find that it's never busy here aside from a few locals.
Is Tenerife or Mallorca better?
I'd choose Mallorca. Palma is a very vibrant city with plenty of shops etc. Playa de Palma is very close to both the airport and Palma, has great beaches and many shops and restaurants / bars. If you don't mind the flight times, then Tenerife would compare favourably for a June trip.