The list you are looking for is available online, thanks to the good
people at golfcourse.com, who have compiled a database of more than
17,000 golf courses in the US.
You can see the list in its entirety (all 17,173 courses!) at:
Because this is such a large list, it may take quite a long time
before it opens up in your browser. Be patient.
You can click on any course on the list for a good deal of additional
information -- # holes, status (public, private, military, etc), year
built, designer, level of difficulty, designer, and so on.
The site for conducting a new search on golf courses -- where you can
select paramaters like state, difficulty level, etc -- can be found
This database should fully meet your needs.
However, before rating this answer, please let me know if you need any
additional information. Just post a Request for Clarification, and
let me know how I can assist you further.
search strategy: Google search on: [ golf courses ]