Question: What is the restaurant Annie and Walter are sitting in that looks out onto the Empire State Building?
Chosen answer: That would be the Rainbow Room which is located at 30 Rockefeller Plaza, the iconic skyscraper in Rockefeller Center.
Super Grover
Question: What is the Big Band song playing as the taxi drives over the bridge?
Chosen answer: It's called Empire State Montage by Hugo W. Friedhofer.
Chosen answer: Ray Charles is the singer who performs this version of "Somewhere over the Rainbow" - this is not on the original movie soundtrack, but you may be able to find a Ray Charles album where this song is included.