Infinity on the Beach. Escape to Infinity on the Beach hotel and discover the best mix of island and beach life in St. Lawrence Gap, Barbados. Situated in a prized oceanfront location on Dover Beach, one of the south coast’s most beautiful beaches, this friendly boutique hotel offers everything today’s modern traveler seeks. The intimate size ensures that you will enjoy unmatched personalized service and attention, and the warm, gracious staff is committed to providing you with the very best of genuine Barbadian culture, cuisine, and activities.