I visited Seoul, South Korea with 2 other friends during the December period (20th December to 12th January).
It was a pretty interesting (budget yet fun) experience that I thought you might be interested to know.

Exchange rate: 822 won : $1 SGD
Travel size: 3
Travel period: 23 days

Total: $2,881.60 ($125.30 per day)

China Eastern Airline (transit at Pu Dong International Airport)
Cost: $700.65 ($2101.95 / 3)
Flight from Changi to Pu Dong was about 5 hours, transit about 2 hours, then another 2 hours flight to Seoul.
The return flight is about the same.
We booked a little late (less than 1 month before departure).
If you booked earlier, it might be a little cheaper.

Airbnb near Mapo Station (fairly central location)
Cost: $938.16 ($2814.50 / 3)
Staying near most of the popular area like Hongdae is pretty lit and convenient.

Sim Card:
Got a 30-day unlimited data-only plan at Seoul Airport.
Cost: $90.21 (71,500 won).
A little costly, apparently my friend told