This is part of the Smithsonian Institution in Washington D.C. Check the current exhibtions to see what is available to see now. You can use the search engine on Events page and type in Japan, China, or Korea to see if there are any lectures, films or other events that interest you. You can also Search the Collections by various ways or just browse the collections by area.
The Met almost always has a special exhibition on East Asian art but you can always go through the galleries of its permanent collection. The galleries can also be visited online . You can look at each room of the permanent collection and view all of the objects in that room. You can also Search the Collections. This allows you to search their entire holdings whether the object is on display or not. You can search by country, artistic medium, artist and other variables. There are currently 17,244 Chinese objects and 21,819 Japanese objects that can be found.
The Asia Society in New York City is interested in art from all of Asia. Besides checking for what their current exhibition(s) are you will also want to see what events they have as they frequently have lectures, films and other events.