Good Dive near Hammerstein Ballroom
My favorite is a place on the north side of 36th St between 8th and 9th, almost to 9th it has some sort of name on the awning, but I doubt that anyone refers to it as such; it is a true dive, but one time some friends and I were sitting in there and some wonderful smell was coming from the kitchen, we inquired as to what it might be and in about 10 minutes were presented with some wonderfully garlicy seafood rice that the owner was making in the back. Although the awning mentions restaurant, that is the only time I've seen any food in there.
There is also the blarney stone just south of the garden but it was recently remodeled and is as undivey as a blarney stone can be, but still cheap and not to bad.
Further down 8th ave is the Penn Place Tavern which is a pretty sleazy dive.
And finally on 9th and 39th you have bellvue and the new Siberia which are fine but a little pricier than the places described above.