Overall, I found that eating well in Jeonju was easy but eating well in Seoul was a bit of a tossup. In Seoul, we were staying by Hongik University, which was a lot of fun and offered easy access to food at all times. In Jeonju I stayed in the Hanok Village and ate both in and out of the village. My abiding impression of food in Korea is that it's often served in massive portions. Completely, utterly, insanely massive.
Gangnam Myun Oak was hands down my favourite meal in Seoul and one of my favourites during the trip. Galbijim and Naengmyeon; both so good!
Nice Two Meat U for tabletop bbq was fun; our friend lives in Seoul so a lot of the time she was leading the way. The sides are totally comfort-food good, like cheesy spaghetti or cheesy mashed potatoes.
Tosokchon for samgyetang. I've never had samgyetang so have no basis for comparison. It was good but I think the dish itself isn't entirely to my taste.
Sulbing for bingsu. This was good, but I like Taiwanese shaved ice better. I think the frozen milk was actually a bit much for me and I like just the regular plain ice base.
Palsaik for tabletop bbq. Eight flavours of pork! It was a lot of fun tasting the different types.
Song Jook Heon for palace cuisine. I don't think it'd be worth the 70,000 won for dinner, but the 40,000 won lunch is not bad. A fun experience; you get to try lots of different dishes.
Gwangjang Market for pancakes. We got ours from a stall right in the centre, but I feel like the ones on the sides were actually better. They looked more interesting.
??? for ganjang genjang. I'd never heard of this dish so made my friend take me someplace I could try it. For anyone else who's never encountered this dish, find a place and try it, it's really good! We went to a place near Hapjeong station.
Veteran for kalguksu. This was awesome; my other favourite meal of the trip probably. I liked this a lot better than what I had in Seoul (Namdaemun's Kalguksu Alley) just because I liked the thinner noodles. Don't worry if there's a line; it moves fast and the place is massive.
PNB for choco pie. I liked the strawberry jam but otherwise liked it the same as a choco pie I picked up in some other random bakery. Don't wait in line at the Hanok Village location; there's another one a few blocks up (north? away from the river) - not on the main street, it's on one of the parallel side streets, just at the edge/outside the Hanok Village. But the best PNB is the big one - if you walk north on the main road that borders the west side of the Hanok Village (by the palace), you'll hit another big road and the big PNB is right at the corner.
Hankookjib for kongnamul haejangguk. This was nice because it was a bit lighter than a lot of the other food I'd been eating.
Banya Dolsotbap for dolsotbap. This was good; I had a mushroom one and like Hankookjib, it was nice to have something non-meaty.
Gyodong Dduk Galbi (?) ddukgalbi place in the middle of the Hanok Village. I liked this but I was sad because earlier I wandered into a ddukgalbi place that seemed awesome but it was minimum two people.
중앙회관 for bibimbap. I have no idea what this translates to but I found it on a blog and it was awesome. There was so much banchan. I love Jeonju and banchan. (blog: http://www.paulajosshi.com/2010/06/be...)
Mt Maisan for pork ribs. I went to a random place that was open and smelled good; this was an excellent decision. If you visit the mountain, you might as well stop for some delicious ribs.
Possibly my favourite discovery of the trip was a drink I had in Jeonju. Moku? I bought a couple cans from a stand - it's an alcoholic beverage and is like a thicker, cinnamon makkoli. So good!
Hope this helps other people with their research!