The park contained a Music Island near the east shore of the Lake. The island was used by musicians who were performing for audiences in the nearby Concert Grove. It was demolished in 1960 to make way for the Wollman Rink. Following the rink's demolition in the early 2010s, a replica of the island was constructed, and it opened in 2012. Across the Lake, two structures were built on the peninsula in the late 19th and early 20th centuries. The Model Yacht Club House, built on the south side of the peninsula in 1900, was an octagonal wood-frame clubhouse that burned down in a fire in 1956. On the opposite or northern side of the peninsula, there was another shelter, similar in design to the Concert Grove Pavilion, which lasted from 1915 to around the 1940s.