What should be underlined or quoted in this sentence?
The Dance of the Sugarplum Fairy is a melody in The Nutcracker Suite.
The nutcracker suite underlined? What about famous dances?
Yes, The Nutcracker Suite is Underlined. Music is in quotation marks.
A case can be made to italicize or underline "The Nutcracker Suite," but music and works of music are not usually italicized or underlined, they are within quotation marks.
"Use italics (underlining) to indicate the titles of books, magazines, newspapers, paintings, and the names of ships, airplanes, and man-made satellites." -- Walsh (1966)