I will have 5 days in Seoul at the end of November and need recommendations for the "must sees". I am interested in experiences that will give me a sense of culture, history and current trends. Also, any recommendations for accommodations? Travelling solo so want to play it relatively safe.

To get a sense of the crazy shopping, I would go to Myeongdong, Apgujeong or Dongdaemun (at night or in the wee hours of the morning). To get a sense of the traditonal/cultural side: Insadong, Gyeongbokgung Palace, War Museum, and Namsangol Hanok Village (folk village). And, I recommend going on the USO DMZ tour. There is a city tour bus that hits most of these places and is relatively inexpensive ($10) or you can master the subway system to get around.

This website http://english.visitkorea.or.kr/enu/index.kto has loads of info. about what to see and do.

Check out my trip report from Seoul.
Nywoman SEA trip Korea. Haven't finished it yet, but Seoul and DMZ are complete.

Seoul i fabulous I loved it.

Do not miss the Noryangin fish market!

and don't miss Red Mango frozen yogurt (you're likely to spot franchise everywhere), food hall at Lotte department store.

Another vote for Insadong (lovely galleries, antique shops, traditional houses, don't miss tea shops--I'm addicted to citron tea). Check the opening hours for palaces--you need to join the tour (English available) for one of them. One of them have changing of the guards in traditional costume.

I suspect end of Nov would be already quite cold. Can probably dip 0C. Make sure you're warmly dressed--complete gear with scarves, gloves, warm socks.