Short answer
Yes, you can go to the beach in the Azores, but most beaches are volcanic dark sand or natural pools. White-sand beaches are rare; the best-known is Praia Formosa on Santa Maria, with other small white-sand coves on the same island. Water is cool even in summer, so check sea conditions and lifeguard coverage before swimming.
General information, not legal or tax advice. Rules and amounts change: confirm with official sources.