Spent almost 2 weeks in ROK in July -- fantastic. The nicest, kindest folks - really amazing!
A couple suggestions:
Much (much) more time in Gyeongju -- I spent 3 nights and it wasn't nearly enough time. Lots and lots to do and see. And that is without side trips, e.g., Andong (but there is Andong jjimdak [wonderful chicken dish] in Gyeongju so you won't miss out if you can't side trip). Rent bicycles -- great way to get around.
Busan - I stayed near the fish market and that was a great area. Near BIFF - street market-ish food area. Easy metro transportation. Stayed 5 days but could have spent a week -- Is a definite must go back to place.
Soju tent/food vendors -- anywhere
UN Korean War cemetery -- above expectations. Very much worth a visit.
A walk along the beach area - very nice. (might be cold?? still a nice walk)
Seoul
Seonjeongneung - burial mound and a neat park in/near Gangnam.
Bongeunsa - a few blocks NE from Seonjeongneung. Fantastic temple complex.
Namsam circuit is nice
Cheonggyecheon - formerly concrete but is now an open river walk -- nice for a stroll
The War Memorial of Korea -- very nice/respectful/classy memorial (IMO)
Visited the Gyeongbokgung and Changdeokgung on culture day ( last wed on month I believe) and it was free admissiona nd lots of folks wearing traditional dress -- really neat. The secret garden - long but worth the time - still requires payment. And one doesn't really need the English (nothing in Danish) tour re I was sold a ticket for a tour later in the day but I just changed it for the Korean tour and walked/looked - the tour is more for the visuals rather than the facts (IMO).
DMZ - took the JSA only tour. Not bad but limited time at the JSA - which seems to be standard for all DMZ tours. The included lunch isn't bad at all (reviewers routinely pan the meal).
Busan to ICN - cheap flights early morning. Cheap flights all day to Gimpo (GMP). I took the train to ICN and it was fine - the flights to ICN were to early (for cheap) and the GMP and then a train (bus?) to ICN idea was not appealing. Paid for business (first - forgot what they're called) class train seats. Nothing special but was worth the modest increased fare (not cheap but not a bank breaker for a long ride).
The idea of TYO to BUS mentioned above is a great way to go. Start at the bottom and work your way north.
As for food, while difficult at times for someone that doesn't speak Korean, it wasn't too bad. Android Google translate works great. But even better was a travel picture dictionary. When I didn't know what "meat" was cooking (sometimes it wasn't meat), I'd point to the animals on the meat page of the book. Then to determine whether it was meat meat or organ meat, I'd point at the picture of organs. Crossing thumb/index finger tips to make a heart (seems to be a thing in Korea) was commonly used to tell me it was organ meat. Pics of vegetables or fish or whatever made food ordering a lot easier. Pantomiming a cow/bull by making horns with my fingers or flapping chicken wings were also successful for finding out what was served --- and by making the food server laugh, it broke the ice and made for a fun meal.
Tokyo - mostly go for sakura (cherry blossoms) but here is my TYO to do list - real short
Menya Musashi ramen in Shinjuku
Godz - nice rock bar - also in Shinjuku (open laaaaaaate)
Cheers -