Seoul is a large city where there are no really center for the city.  Places for stay can vary from Airbnb to family run guesthouse, hostel and hotel.

MyeongDong

The second best choice of area to stay is at Myeong-Dong. Typically tourist will choose to stay in Myeongdong ans this area is centrally located in Seoul. It is easier to access other districts in Seoul from Myeongdong. This area is very popular for shopping and foods.

Gangnam

The most expansive area starts from Gangnam where it is made famous by the popular Gangnam style song, Psy. Gangnam is one of the most upper class are in Seoul. This area is also popular if you plan to do your plastic surgery in Korea.

Hongdae

This district has a combination of arts, shopping and many more. This place is probably something like a hippie place in Seoul. This place have a good combination of cafes, clubs , restaurants and art museums.

Hongdae can be reached by HongHik University Station on Seoul Subway Line 2

Insadong

Insadong is the cultural district of Seoul where all the traditional attractions are located. This is a very touristic place where you can find old Korean buildings , palaces and small traditional tea house. This area is a little north of Seoul.

This place can be reached via Anguk Station (Seoul Subway line 3 . E6) or Jonggak Station (Seoul Subway line 1. E3)

Food

There are no worries for food as there are plenty of Korean restaurants in Seoul.