Adding to mclaurie's and EmilyC's comments, the take-away shops are on the Concourse Level in the Rockefeller Center itself. IIRC, in addition the places already mentioned, there's also a Pret a Manger. The European-style cafe that Emily mentions has a wide variety of choices. As at a food court, there are tables and chairs in a common area, here, looking out to the skating rink.

That's the name - "pret a Manger" - ready to eat!!! I could not remember it..

On this page you will find a drop-down menu which lists and links to the restaurants at Rockefeller Center. Take a look at the On The Go selections.

http://www.rockefellercenter.com/index.php/section/3