If you are creating a console application? Stderr is the standard way to log errors. Let the user decide if where it points to.
If you are creating a daemon, set the log destiny at the launch script. The application can either log to stderr anyway and let the script handle everything, or offer a parameter for setting the log channel.
The Java community fixation on logging is really not deserved. It's more caused by bad error handling by their main web servers than by any fundamental problem.