You can define the default home directory for all Cygwin users in the nsswitch.conf file.

For example, the following sets your default home directory to /cygdrive/c/Users/{user_name}/home, or in Windows notation to C:\Users\{user_name}\home.

db_home: /%H/home

You can change it to whatever you like.

See the Cygwin documentation for more information. Look here below the /path section for more on supported wildcard characters.