PaulS:
Would you care to elaborate?
There is one serial port. Serial.write() and Serial.print() are two ways of sending data to the serial port. They are not ways of directing data to one device listening to the serial port versus the other device.
There should only be one device (either the PC and the Serial Monitor application or the XBee.
If you need two serial ports, you either need different hardware (like a Mega with 4 hardware serial ports) or different software (SoftwareSerial, to create a software port).
Thank you Paul. This actually means that once I run my code w/o being connected to the PC, and w/o Serial.write this should work. This - if I understand correctly - is good news. Thank you very much for clearing this out.
If on the other hand I'm missing something again - please let me know.