There is a wonderful tool, developed by some colleagues at the Harvard
Cultural Observatory in association with Google, that applies some
genomics techniques to culture.  They take advantage of the huge Google
book scanning project to let you look at the occurrence of words or
phrases in a deep sampling of everything published in English over the
last several hundred years.  (Beware -- it is quite a time-waster once
you get into it!)  You will find one of the most useful tools, the
ngram viewer at  http://books.google.com/ngrams 

If you search for "nickelodeon" you will see that the word first came
into use in about 1905, peaked, dipped in the 1920s, and then skyrocketed
in about 1940.  All the references before 1940 seem to be to a movie
theater; sometime between 1940 and 1945 it began to be used to describe
a music machine (so definitely predating the "Put another nickel in"
song's popularity), I haven't taken the time to try to track it down
exactly.

It is quite interesting to look at how words like nickelodeon, juke
box, orchestrion, player piano have come and gone from our written word
over time -- be aware, though, that most current uses of the word
nickelodeon refer to a TV channel, not a music machine or theater!

Cheers!
Roger Wiegand
http://www.carouselorgan.com/