I lived in Seocho (Seorae Maeul) for a year, right next to the school on the hilltop. It's a good area, quiet and very clean, with a bunch of various western eateries and a small shop to buy western food and non-food items. You can also go near the top of the hill and play soccer or whatever on the open field. I recommend it after reading what your plans on for your future with your family.
The only bad part is that the subway isn't super close like you can find in a lot of places in Seoul. |