Probably European think that oyster is a food which is eaten as raw. This is an interesting thing due to Japanese love raw seafood=sushi but do not eat uncooked oyster so much as European. On the other hand, European do not eat other raw seafood as Japanese do.
One of the typical ways to eat oyster in Japan is fried oyster. Oyster with breadcrumbs is deep fried and eaten with sauce. Then, another way is a grilled oyster. Oysters are put on a gridiron and grilled on charcoals.
Griller oyster can be eaten everywhere. Either you have to buy a gridiron and charcoal or go to a specialized restaurant which is called oyster hut. Oyster hut is as same as Japanese BBQ(Yakiniku) or Korean BBQ restaurants, you have to grill the oysters by yourself.
Choose the ingredients including oysters and there will be also a table charge per group. Some oyster huts allow you to bring snacks and beverage with you.