Have you been to Tongin Market for the lunchbox cafe? You pay like 6,000W and get an empty plate with some tokens and can go around the market and fill up your tray with whatever you want.

Also, Gongdeok Market? I know Gwangjin Market has the main drag of tourist places, BUT within the market and the surrounding alleys are some amazing Beef Sashimi places. Also, I found a great Garlic Dak Bokkeumtang place randomly in a back alley of Jongno.

One idea for food (and you'll need your wife's Korean help)... there's a chef here, Baek Jeong Won, who runs a giant operation of popular chain restaurants. Meat, soups, etc. Wildly popular. BUT, what's more important is that he has several TV shows now. On these shows, he goes to random restaurants and makes his "list" of places he recommends. Yes, it's featured on TV, but they are certainly random restaurants you or most Koreans have never visited. Maybe that could give you some guidance.

Honestly, the food markets don't really change. They've all been there forever selling the same stuff haha.

And yes, the heat and humidity right now is GROSS. And I'm from the Southeastern US. I mean if you're visiting and you have to be outside, you just have to bear it. But prepare for an evening shower or change of clothes if you're out all day. Your clothes will be soaked.

If you want, I can certainly recommend you a ton of random places I go to eat that are local, popular, and delicious. Send me a PM if so.