My visiting out-of-town girlfriend and I had a hilarious time being scrubbed raw at the Beverly Hot Springs in K-town last year and are going back tomorrow for more punishment at the Olympic Spa. We're chowies, but please excuse that we're completely ignorant about Korean food. When we tried somewhere to lunch last year, the restaurant was beautiful but the waitress was not helpful/happy and we chose food we didn't enjoy; giant bowls of bland noodles in broth. We won't be fooled again.
I've seen Koreatown Plaza recommended on this board and it's nearby the spa and sounds like great fun. I believe there are small restaurants/stalls so we have a chance of seeing food before we order. May I please confirm that we can sit and eat and this isn't just a market or take-out venue? Thanks so much.
Across the street from Plaza Market is Ma Dang which has some of my favorite noodles ever! Definitely not bland IMHO. I go there all the time and get one of two things: the chicken kalgooksoo or the kimchi kalgooksoo. Never eaten in the food court at either markets though so while I couldn't compare, I'd definitely recommend Ma Dang since it seems nearby to your spa also.
Koreatown Plaza and Galleria Market (a block south of Koreatown Plaza) have food court systems - you pay for the food first, pick it up when it's ready and you grab a table. For most part the food stalls have picture menus on the wall so you won't be surprised by what you order.
Have fun at the spa!