I've dined at the Japanese and French restaurants at The Shilla and both are very good. The hotel is owned by Samsung and run by the eldest daughter of its former chairman, so you can be sure that the restaurants are in tip-top shape. They have an impressive wine list.
Otherwise I patronize the restaurants in the basement (two floors) of Seoul Finance Plaza just behind the old city hall (which is unfortunately being torn down). They offer several fine dining choices: Japanese/Japanese fusion, Italian, Chinese fusion (pine mushrooms and abalone to die for), Shanghainese, Indian. This is not your run-of-the-mill food court type cuiside. Sushi in Seoul is as good as Tokyo but at half the price.