Seoul Station
Seoul station has 5 subway lines and KTX train to Busan.
Line1, Line4, Airport rail road, Gyeongui-Jungang line. There is huge Lotte Mart and outlet at Seoul station.
Airport train directly comes to seoul station.
ICN airport - 45 min
Gimpo airport - 20 min.
It is very safe area with a lot of eatery, shopping and taxes. You can walk to Myeongdong and Namdaemun. 5 -20 min subway to Hongdae, Dongdaemun, Shinchon, Ehwa woman's univ, Itewon, Gwanghwamun, City hall.
Also there is train to Nami island and KTX for Busan.
Myeongdong
Most crowded and lively shopping and eating area. Full of shops, street foods, restaurants. Many cosmetic shops.
15 min walking
2 min subway line 4.
3 min taxi basic fare.
Hongdae
Most fun, crazy and cool area near Hongik Univ. It is mixture of young and energetic cultural place. All kind of music clubs and live bars. A lot of eateries and shops. Night party never ends. Also many relaxing cafes. It is huge area which has 3 subway station. Hongik Univ sta.(airport rail road, line2, Geyongui), Sangsu sta.(line2 &6), Hapjeong sta.(line6).
10 min subway Airport line.
Namdaemun Market
Very old and cheap market where you can find everything. Huge market for clothing, glasses, kitchen ware, toys, grocery, accessory, shoes, bags etc. Kalchi jorim(spicy fish stew) is very famous. You can get glasses with lenses without prescription in 30 min with amazing price.
10 min walking.
Dongdaemun Market
24 hours market area. You can buy clothings, accessories, shoes etc for whole sale marke. A lot of eatery around buildings. After 10 pm you can have better deal. You will never get bored shopping here as tones of nice fashion itemes please you with amazing price. Local girls like Jeil Pyunghwa, U us and Pyunghwa market than other buildings. Chungpyunghwa is amazing for whole sale shopping. For amazing price fur coat try Kwanghee market.
15min subway line 4.