This should be fairly easy in LabVIEW. You will use VISA to read the from the serial port and write the output string to a file.
I created a quick example that will demonstrate this. First create a loopback cable (short pin 2 to 3 on a DB9 connector). Then run the VI and select a text file to send and save the file you receive. Since you will have another computer doing the sending your VI would be pretty much the same just without the VISA write.
Shawn B.
National Instruments