I think everyone's pretty familiar with the restaurants on 32nd street (between 5th and 6th) that have been there forever. I think all of them get tons of business primarily based on their location. I think that because they don't have to worry about not getting business, most of them are complacent and have pretty iffy food.
I'd written something in response to a question about 24 hour places, but I realized that there were tons of restuarants that I'd forgotten to mention that I think also have some great food and wanted to at least mention them. (All of them are not on 32nd Street between 5th and 6th.)
We found a place called Donuibogam last year (it's located on 32nd east of 5th Avenue on the north side of the street--big white building with a huge front window--new and very clean). This place is super-popular and seems to be doing very well, including tons of customers who are not Korean--super popular among Americans because, I suspect, it's really clean and nice on the inside and the place has a huge wine list (although we usually only drink beer and wine). The barbecue here is really good, though, and the side-dishes are pretty darn good as well. When you're looking for a giant barbecue-based meal, this would be my recommendation. Try the samgyupsal (pork belly). It's one of their specialties and is wine-marinated which is apparently the trend in Korea recently. Also, the other thing I love about this place is they actually care about their banchan (side dishes)--it's really good and there are many different types. Be prepared to spend money if you go here though, because you'll most likely end up ordering a lot.
Another recommendation for barbecue is 36th Street Barbecue (between 5th and 6th on 36th). They do banchan very well and they obviously take great care in preparing their food. My only criticism is that their food is a little sweet for my tastes. My wife is a fan of their desserts.
I wrote a review of Yangpyung (which is on 33rd Street east of Broadway/6th Avenue on the north side of the street) in response to another post, so I'll just summarize here. This is a recent favorite of my wife and me. Great banchan (although it's just six or so types--quality is key, not quantity) and great food. Best mandoo in Manhattan, in my opinion (better than Mandoo bar, I think). This place seems to always be kind of empty, and we hope it does well so that we always have the option to eat there. Their service is very good/friendly. My wife and I are going to eat every item on their menu. We've been very, very happy with our meals there. This place may very well be tops for Korean soups in Manhattan. Anyway, I hope this place remains a fixture on the restaurant scene in Manhattan. Quality should be rewarded.