Michael Pollak in the FYI column of the New York Times has the answer:
How did the block of 46th Street west of Eighth Avenue become Restaurant Row? Why not 47th Street, or 45th Street?
A. “It was just a good strip,” said Mary Brendle, the community district historian for Hell’s Kitchen and Chelsea.
According to Ms. Brendle, West 46th had a fairly consistent line of rooming houses — some still exist — with zoning that allowed commercial activity on the first floor, perfect for a wall of restaurants just a block from Broadway theaters. The commercial space survived waves of high-rise development. Today, she said, the strip, as part of the Clinton preservation area from 43rd to 56th Street, and from 150 feet west of Eighth Avenue to 10th Avenue, is protected by low-rise zoning.
The designation Restaurant Row for the block between Eighth and Ninth Avenues was made official in 1973. “Where else in the world, except possibly Paris, could you get 16 of the best restaurants collected in such a short strip of land?” Mayor John Lindsay said at the dedication.