Unfortunately, there is no actual soundtrack album, "A Kind of Magic" is the closest thing to it. Like AzureKite mentioned, "Hammer to Fall" is on "The Works" and "New York, New York" was never actually released on any albums or singles.
"New York, New York " is on the "Highlander (Complete Original Motion Picture Score)" CD which doesn't include some of the other Queen songs from the movie though. :p But even then "New York, New York" is not a complete song as far as I've heard.
I nearly bought the score when i was in Japan but I was a little low on money and not completely thrilled with the CD description, so I don't have it.
A full length recording of "New York, New York" does exist (Brian May has it), but what appears on the score album is just the same short snippet that appeared in the movie.
The Show Must Go On recording process
"Mercury was so ill, and could barely walk, when the band recorded the song in 1990, that May had concerns as to whether he was physically capable of singing it. [...] Demo versions featured May singing, having to sing some parts in falsetto because they were too high. When Brian May presented the final demo to Mercury, he had doubts that Mercury would be physically capable of singing the song's highly demanding vocal line, due to the extent of his illness at the time. To May's surprise, when the time came to record the vocals, Mercury consumed a measure of vodka and said "I'll fuckin do it, darling!" then proceeded to perform the vocal line in one take without problems."
I think that says it all...
I'm not ashamed to admit, I cried the first time I heard that song.