Free (Suggested) Admission on Monday at the The Met Cloisters - see INFO below. The Met Cloisters, located on four acres overlooking the Hudson River in northern Manhattan's Fort Tryon Park, is the branch of the Museum dedicated to the art, architecture, and gardens of medieval Europe. Deriving its name from the medieval cloisters that form the core of the building, it presents a harmonious and evocative setting for more than 2,000 exceptional artworks and architectural elements from the medieval West. More Info below.