There is no Belvidere Park located in the state of Missouri. It is possible that the Belvidere Park in Illinois is being referred to, which is a popular recreational area that offers a variety of activities such as fishing, boating, and picnicking. The park also has several points of interest including a historic lagoon, a butterfly garden, and a walking trail. It is open year-round, and the best time to visit would depend on personal preference, as the park offers different experiences during each season.