What are fun things to do during a visit to South Korea?

I will be near Seoul in June. I doubt that I will have a car available for personal use.

Try and get to Seoul somehow. Head for the Olympic Park. I spent a whole afternoon looking at the statues there once. Also Lotte World, Dongdaemun market, Namdaemun market, Itaewon and Chenggaecheon etc.

Have a look at -
www.korea.net or www.tour2korea.com

Have their food, try to speak with them in English. What better than that? You'll atleast teach them few words with what they can manage the next guy.

transportation is absolutely no problem in SK.
you can get the subway, train, bus, or whatever to Seoul - if you want to come here.
You don't say exactly where you will be so ....

I think you should go to Everland. Unlike Disneyland, you can drink beer there. It's great. I have a great story about the first time I went there, but I won't tell it here... since it's not part of the question.

Go to Cheju Island

Visit theme parks (Lotte World or Everland), Korean Folk Village, Insa-dong for fun.

Myeong Dong, Dongdaemoon, Namdaemoon, Lee Tae Won for shopping.

Eat some Korean bbq, street foods etc, go to shinchon, Hong Dae Ip Gu for drinking etc.

Eat fried dog.....eat some more fried dog...

You could try dodging the secret police that will be watching you everywhere you go.
Or start an uprising of some sort.
Oh what fun youll have after being beaten with that rubber hose in prison. xx