I had the same issue on a new bike after @ 100 miles. After systematically removing bottle cages, pump, re-greasing pedals and bottom bracket, I finally traced it to the two machine screws that attach the derailleur hanger. Seems they came loose during those 100 miles and probably weren't tightened enough in the first place.

The problem with clicks is they resonate through the frame, making it really difficult to trace.