Oh, where to start...First of all, congratulations, I just know you're going to have a great time!
I liked Namsan Tower, Gyeongbokgung Palace, and Insadong. If you want to try a jimjilbang (I really recommend it!), Dragon Hill Spa is awesome (don't forget to also get baked eggs and the rice drink while you're there!).
For food...egg bread is delicious so if you see it being sold, (and you aren't allergic to eggs) you should definitely try some! Really, all the street food is fun to try. :) We also tried samgyopsal (a chicken soup thingy, really yummy!) and Korean BBQ, or course! If there was a day we weren't feeling adventurous, usually we could rely on Seven's chicken restaurant for some yummy chicken and noodles--there are a few of them scattered around Seoul. But really, try as many different foods as you can. Oh, and ddeokbokki! That's a good meal too!
Also shopping in Myeongdong can be fun (I also went with a few friends to see NANTA there), and it's better to visit Hongdae at night. If you go to Gangnam, Coex Mall and Bogeunsa (sp?) temple are right across from each other and both are really cool places to visit. And if you're not opposed to lots of walking, there's also the Olympic park, and all the floors of Shinsegae Dept Store (waiting for the elevators takes forever--take the escalators, and there's a nice rooftop park kind of area on...the 7th floor if I remember correctly? With a Starbucks and some other restaurant)
I stayed at Ewha, and the area is probably one of the cheapest places to shop (for the college students) and it's also a really cool place in general. There are also a lot of yummy restaurants there.
If you like museums, the Seoul National Museum of Korea is really cool.
Oh, and don't forget Chongyecheon (argh spelling) stream...though my friends and I had a hard time finding a good place to eat around there. And then there's the Han River too.