The Statue of Liberty stands on Liberty Island in New York Harbour, visible from lower Manhattan and the Staten Island Ferry. The crown and torch are accessible only by advance reservation (book weeks ahead in summer); the grounds and museum are accessible with a ferry ticket alone. The ferry from Battery Park takes about 15 minutes and the trip across the harbour is itself one of the better experiences in New York.
Ellis Island, on the same ferry route, holds the Immigration Museum in the old main building. The Great Hall, where millions of immigrants were processed on arrival, is a genuinely moving space, and the museum's exhibitions on the experience of arriving in America are well done. The combination of Liberty Island and Ellis Island takes most of a day. Book ferry tickets and crown access well in advance, especially in summer.