The recommended option for showing log info (such as stacktraces) is to create your own logger.
Simply call
Core.getLogger("MartinsStacktraceLogger").info("my error message")
and it'll show up in your logs. Optionally, you can add an extra parameter of type Exception:
catch (Exception e) {
Core.getLogger("MartinsStacktraceLogger").info("my error message", e);
}
which will then also include the entire stacktrace in the log message.
To answer your original question (where does the console output go), it depends on where you're running the runtime from. If you run it in eclipse, it'll show up in the eclipse console output. The modeler simply doesn't show the console output.
You can easily obtain the stacktrace of an exception using the following java code:
String stack = "";
if (e != null)
stack = org.apache.commons.lang.exception.ExceptionUtils.getStackTrace(e);