Boo, I'll be in NYC from 8/1-8/9. When are you here?
Avoid Itaewon like the PLAGUE. Unless you like douchebag frat boys who outnumber Korean people 10:1.
Go to Hongdae- It's young, hip and cheap. Bar Da makes an apocalyptic and wonderful Long Island Iced Tea. FF is a cool dance club. Ting Tings isn't bad. The rest of the clubs tend to be really expensive, shitty versions of Euro/American clubs.
Right next to Hongdae is an area called Hapjeong that's pretty cool. There's a bar there called Bau-haus that has dogs you can pet and play with. There's also a bar that looks like a European cathedral on the outside and a Bavarian drinking hall on the inside. Kinda pricey, but nice to see?
Lotte World rules. BobFromPikesCreek & I went two weeks ago. Go to Seoul Tower at night if the weather is clear. It's really pretty. Avoid the restaurants there, although the Italian place at the bottom isn't too pricey. If you wanna do shopping I have 3 suggestions:
Insadong, near City Hall, for cheap touristy stuff. Insadong is also home to the COOLEST TEA CAFE EVER. It's decorated like a train and then the rest of the restaurant is like a mini village. It's hard to explain. Apujyeong if you wanna see the 5th Avenue of Korea (They have a ROLLS ROYCE DEALERSHIP ffs). Gangnam if you want something in the middle. Although, most major areas have some kind of big market space for shopping, although some are way more modern than others.
Look for a traditional market somewhere. Namdaemun is kind of neat, but touristy and not that traditional anymore. You may have to poke your nose a little ways outside of Seoul to find one.
I'd avoid the museums. They tend to have little to no English in them and always feel kind of anemic to me.
Food-wise: Look for a chicken galbi chain called "Yogane". It's the fucking jam- Order the cheese stuffed dukboki. There's a restaurant in Gangnam called STAR CHEF that's seriously amazing- Korean food with a French high-culinary twist. Kind of pricey (Entrees start around 20-30$), but the portions are fucking enormous.
Most of the traveling/tour-y stuff I've done has been outside Seoul, so I'm kind of helpless here. Just eat whatever you see on the street, drink weird shit from the c-stores and have fun.