If you want copious amounts of overpriced, fatty, fattening, overrated food, then by all means go to the Stage or Carnegie.
On the other hand, if you want excellent Greek seafood, go to Molyvos, 871 Seventh Ave., between 55th and 56th. Just two blocks from the Hilton is Beacon on West 56th St., just west of 6th. Really good Continental menu. Neither place is cheap, but worth the tab.
If you want to spend less and have one of the best hamburgers anywhere, check out The Burger Joint in Le Parker Meridien on West 56th between 6th and 7th. No ambience, but the food's great, provided you want a hamburger.
On the same block, at 121 West 56th, is Topaz Thai, very respectable Thai food at prices well below the norm for this neighborhood.