No one talks about Christmas in Korea, because it's an imported holiday for the worship of Jesus' B-day and crass commercialism. Like impolyt and naehun wrote, Christmas isn't a national holiday, and armed with one extra day off from work (if they have the day off at all), most Koreans are going to pack into already overcrowded shopping malls or overbook most decent restaurants before getting back to the daily grind. Basically, outside of some Christmas-themed lighting installations here and there, and multiple performances of Handel's Messiah
, don't expect much pomp surrounding Christmas even in Seoul.
That said, there's fun shit to do in Seoul whether its Christmas or not:
- check out the palaces (esp. Kyungbok, Changdeok, and Deoksu)
- go through theme-y neighborhoods like Samchong-dong/ Gahoe-dong (art and food), Insa-dong (arts and crafts), Hongdae (clubs and japanese otaku shit), the park area near Apgujeong (star-watching)
- visit the Leeum Museum, or if you've got time, the Seoul Museum of Art, the Seoul Arts Center, or the National Museum of Art
- go hiking (if there's no snow) along Bukhansan and look down on the Blue House
- there might be some decent concerts or festivals going on at the time, and you can always go clubbing around Gangnam or get drunk with socially awkward ex-pats in Itaewon
- check out the DMZ (which is kind of creepy, actually, but might be the most decked out place for Christmas in all Korea) and the Korean War museum, if you're a war history buff or like the kitsch of anti-commie agitprop
- go shopping in overcrowded shopping malls like Lotte, Hyundai, and Sinsaegae and then compare it to cramped "traditional" markets like the Namdaemun and Dondaemun sijang(s)
- wander around all day, get lost, eat lots of strange food, get drunk on soju, try to score some off your gf in a love motel (as has been covered)
But...that's Seoul. I assume that your gf is Korean or Korean-American (or Korean-[insert nationality]), which is why you're spending Christmas in Korea. I then assume that she has parents/ relatives in freezing-ass Daegu, which is why you're staying there instead of Seoul over Christmas. I don't know what you could possibly do for an extended period of time in Daegu during the winter except drink soju and hope your gf has cool relatives who speak English well. Instead, try and get outside of Daegu as much as possible (either drive around with one of her cool relatives or bring an international drivers license and rent a car together), and check out the former Silla capital in Gyeongju, drive along the eastern coast stopping at some of the small towns for seafood, etc. Most of the interesting things you can do in Daegu or Busan - eat sashimi, visit the beach on a blustery day, check out Buddhist temples and historical sites - you can do better and cheaper in the Gyeongsang Province countryside. Busan can be a fun city, imho, but if your time is short, I recommend visiting Seoul for your city-fix, and checking out some of the rural sites around Daegu for everything else.
Here's a link to some of the "theme courses" you can check out in Daegu: http://english.daegu.go.kr/cms/cms.asp?Menu=490