Yes, tickets for Statue Cruises can typically be purchased on the day of your visit. Visitors have the option to buy tickets at the various departure locations, which include Battery Park in New York and Liberty State Park in New Jersey. However, it is important to note that during peak times, such as weekends and holidays, demand can be high, and it is possible that tickets may sell out. Therefore, it is advisable for visitors to arrive early in order to secure their tickets and enjoy their experience without any concerns. For the most accurate and current information regarding ticket availability or any specific procedures, it is a good idea to check the Statue Cruises website.