Seoul in particular and South Korea in general is a nice place to spend a New Year's Eve because the government of South Korea takes special measures to make it a wonderful and memorable day for all. Hundreds of free events, concerts, special dinner tables at Top Hotels and firework displays are all around the city and one such Fire Work Display is at Han River - the same spot as before here.
Traditionally Koreans go to small islands such as Khoje-do or Ganghwa-do etc. (check this list of 30 plus islands where you can see the sunrise and enjoy breathtaking scenes) to witness the sunset and spend night there and then witness the first sunrise. They have a breakfast of Ttoekkuk (Rice cake noodles) and they believe that doing so will bring good-luck to them!
If you don't want all that hassle then you can simply go to Jongnu where we have Jogya Temple and very close to it is Insa-dong (definitely visit Jongno's official page)and see the display of Bosingak or Ringing of the Bell Ceremony at midnight sharp, in attendance are the headmonk of Won- Buddhism and the President of South Korea and thousands of people. Special subways run late in the hours. This is also a venue for open concerts and many other events. It is worth spending a very cold but otherwise warm and exciting evening.
Ritz Carlton has a very fantastic concert every year so check that out too. DJs from around the world heads to Seoul so one call Seoul Global Center for more information. Seoul Global Village Help Centers also organize many events.
A concert is also organized at Samcheonggak- with a beautiful venue to look at Seoul's dusk and dawn on Dec.31st, 2011.
If you are at the Namsan Tower, you can enjoy several firework shows all over the city at the same time such as at Han Bridges, Seoul Plaza and also at the Yongsan Base etc.
You can take a Night ride of the Seoul Tour Bus and see how the city is decorated.
A lot of people like to cover, Hongik, Itaewon, Apgujeon and Gangnam - the same night so that they do NOT miss a thing anywhere. Try to use public transport to avoid traffic jams.
2012 is the year of the Dragon and some in my family will welcome this year more than others because they were born in the year of Dragon which is going to be back 12 years later, it signifies enlightenment, happiness, self-sufficiency and success.
I hope that this year brings the good things of life & particularly health, prosperity and peace of mind!
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