Must Go/See/Visit Places in Seoul

There are lots of travel guides on Seoul but here is a summary of a list of must-visit places in Seoul. The reason why I am excluding an itinerary is because the places are well within reach of subways and one can plan based on the subway maps depending on their personal preferences (shopping? sightseeing? etc).

Shopping: 

Myeongdong (cosmetics and clothes)

Yeongdeungpo Underground Mall (sheltered thus good place to shop if raining)

Seoul Bus Express Terminal (underground shopping)

Ewha (University shopping street, mainly clothes and bag)

Hongdae (University shopping street, mainly clothes and bag)

Dongdaemun (open till late but I don't like shopping here as you need to haggle)

Namdaemun (more like a marketplace, for getting cutlery, souvenirs, idol stuff etc)

Lotte Supermarket at Seoul station (Korean groceries)

Sightseeing:

Nami Island

Namsan Tower (near Myeongdong)

Gyeongbokgung (near Gwanghwamun, rent a hanbok nearby and you can enter for free)

Cheonggyecheon stream (near Gwanghwamun)

Yeouido (good place to catch fireworks festival and cherry blossoms)

Banpo bridge rainbow fountain (take a cruise from Yeouido)

Gangchon rail bike

Activities:

Yongsan Dragon Hill Spa (jjimjilbang located at Yongsan station)

Lotte World (theme park located at Jamsil station)

Yongin Everland (theme park located at outskirt of Seoul)

December/January is a good time to head to the ski resort in Gangwondo. You can consider Vivaldi ski park http://english.visitkorea.or.kr/enu/ATR/SI_EN_3_1_1_1.jsp?cid=266845. This ski park offers night time ski, good quality snow and the slope side condos are fantastic. It also offers free shuttle bus services for foreigners, from Seoul.