Fascinating place IME, and a good side-trip from SG. Maybe better for people considering it to avoid winter, as I recall it gets pretty bitterly cold.
TripAdvisor is good for these kind of broad questions, esp where your own specific tastes and budget are unknown.
Here's their member rated restaurant suggestions for Seoul. The nice thing is the rankings can then be filtered by budget, cuisine, neighbourhood, and so on. The number of 'Certificates of Excellence' awarded from just the first page of hits bodes veery well indeed!
https://www.tripadvisor.com/Restaurants ... Seoul.html
From that page it's just a click away to 'Things to do', and similar member ratings.
I like and use TA a lot. Even to find suggestions for things to do in my current city, and I always use it if I'm visiting somewhere new to me. They have a *very* strict policy of fake up-ranking, so I trust their listings. Also you can read the individual member reviews for lots of detail, which dishes they suggest are must-haves etc, and also see a mini-bio of that reviewer, so you get a feel for that reviewer age/demographic/likely budget, and so on. IME it's one of the more useful free and unbiased review sites out there.
[Note: I have been a member for several years, and have submitted many reviews from around the world. Membership is free, the trusted exchange of reviews is what it's all about. The only thing thing I've got from them beyond insight, was a TA logo'd luggage tag. That was after something like my first 50 reviews. It can be fun to have in view on a suitcase or daypack when entering a restaurant or hotel - i.e. most such places know that logo, and that a person with one is likely well travelled and perhaps approaches things with a 'reviewers mindset'.