Where are Cygwin installer settings stored?

The only setting that Cygwin setup is storing on the Register is the location of the various installations at

Computer\HKEY_CURRENT_USER\SOFTWARE\Cygwin\Installations

Usually the defaults are

C:\cygwin       (for the 32 bit version)
C:\cygwin64     (for the 64 bit version)

You can tell anyway Setup to use a different directory or disk, setting a different Root directory.