So far the two I've accomplished have been food related. Both items are uniquely Korean, or at least uniquely Asian, food combinations you just won't find in the U.S., or at least I've never seen them there.
The first is 피자 돈까스 (pizza donkkaseu) a variation on tonkatsu (Japanese breaded, fried pork cutlet). Regular donkkaseu has been a comfort food favorite for most of my time in Korea. I wasn't so sure about the addition of pizza cheese (mozzarella) and (in one of the versions I tried) corn would make it better. It actually does. I had to order it a third time, just so I could take a picture. The first time, we ordered in and I was so hungry by the time the food came that I couldn't wait long enough to take a picture. The second time, I ended up with take-out (that's what happens when two moms with two toddlers and two babies try to dine out), so it was already cut into bite-size pieces. (Most Koreans apparently do not own knives and forks, so take-out is made to be eaten with the chopsticks and spoons that everyone is sure to have.) I think I'm done now, though. Consuming that much fat in one meal does not sit very well with my stomach.
Pizza donkkaseu (served with rice, room temperature corn, cherry tomatoes, and shredded cabbage with pink sauce (AKA ghetto 1000 Island; ketchup & mayonnaise):

A close up of the cheesy goodness inside. Another version is called 치즈 돈까스 (cheese donkkaseu) which has a slice of processed cheese (i.e. "American" cheese) either on top or inside. No thanks.

My second "I really have to try that before I leave Korea" food was a corn dog and fries...together...like one solid piece. I don't actually know what it's called. I always see them being served up at carts near the beach or stands at Mt. Seorak. At first, I thought it just looked weird. Another variation on the corn dog here includes dipping the finished product in chocolate and sprinkles. Seriously. But the more I thought about it, the more it made sense. Why bother having two separate items when you could just have a complete meal on a stick? Y'know...minus any actual vegetables -- do fried potatoes really count? -- or fruit or...well, you get the idea. Health food this is not. (Note the concerned look on Rowan's face. Liam doesn't really want anything to do with it.)

The vendors prepare them ahead of time, then fry it again to freshen it up a bit, before drizzling ketchup over the concoction and serving. Liam almost...but not quite...took a bite. Again, it was actually pretty good, but I don't plan to eat it again because it's not exactly (how you say?) "good for me."

As for the rest of my list, the parts I haven't done yet...there's only one thing:
see a palace or something similarly historic and royal and stuff
I've wanted to do this for a long time. On our one-week, whirlwind tour of the peninsula (or at least the coastline) in July 2006, we went to 경복궁(Gyeongbokgung), but were foiled by torrential rain. 창덕궁 (Changdeokgung) is actually supposed to be more impressive, but can only be seen on a guided tour (3 per day according to Lonely Planet). We'll be in Seoul two weekends from now with my in-laws, so I'm hoping to tour one of those (or another, if anyone has a recommendation) then.
I've been told repeatedly that I should visit a 찜질방 (Jjimjilbang -- public bath house), but I'm just not interested. To say that I'm not into public nudity is an understatement. I waived my P.E. requirements in high school, not because of religious reasons as the waiver request said, but because I HATED showering in front of my classmates. I know that I should be over that now that I'm over thirty and have gone through pregnancy and birth twice, but the idea of old Korean ladies staring at me, and possibly poking and prodding my wobbly bits (a friend has a hilarious, but horrifying story of her jjimjilbang experience) does not excite me.
If anyone has suggestions of other things I should do/see while I'm here, I'd love to hear them. (Just as long as they don't involve public nudity.)