Barbados has plenty of beautiful white sand beaches. The best beaches can be found along the Caribbean (southwestern) coast. Here you can find long stretches of white sand and calm waters. However this is also the area where most of the beach resorts are located. The closest beach to Villa Horizon is Colony Club Beach, which is located ~1km from the villa.
All beaches are 'public' although sometimes you have to cross the property of the hotels. A large part of the north, southeast, and east coasts have steep limestone cliffs, but in between those small private sandy coves with palmtrees can be found. Be careful with swimming though, currents and undertow can be strong on the east side of the island.
Quiet sand beaches can also be found on the northwestern coast, such as, Horseshoe Bay, Cluff's Bay or Archers's Bay; these are only accessible by secondary paved/unpaved roads. Crane Bay on the southeast is probably one of the most beautiful beaches on the island, but the waves can be quite rough at times.
