I recommend Masan Yangdeok <Seoul Children's Hospital>.

My nephew was admitted to the pediatrics department of Masan Yangdeok Seoul Children's Hospital a few days ago complaining of high fever and severe lower abdominal pain. He's currently receiving treatment there, so I visited him today. The hospital has an inpatient ward, so the facilities are nice, and the staff is friendly. The pediatrician is excellent, and it's a well-known pediatric clinic, so I highly recommend it.