Interesting place to go for a week?!?
I lived is S Korea for 2 years,
Best advice is to go to the tourist info and they will prob plan your trip for you. Seoul is a v big city, go to some of the markets, I think one is called namdaemun, if ia am remembering correctly.
Also go to a galbi restaurant, drink some soju, maeshil ju (plum wine)...
Outside of Seoul - climb some mountains and visit the temples at the top?!
We use to go to Itaewon when we went to Seoul because it is quite Westernised (lots of American soldiers aswell though. Western bars etc, about 10,000won for a pint of guinness (dont know what it is now).
Souvenirs..mmmm pottery (soju cups) are always nice, masks - but i think it you havent been to the Andong folk village (central Korea - yuo could go by bus)they might not seem very interesting.
Hope this is of some help?!