I had both experiences: first I killed about 25 spiders and gave up.  Next I abandoned the quest, took it up again and immediately went to the locations given by other posters (thanks!).  Success on the first kill!  The key, I think, is to get to work right after accepting the quest.

It seems like this might be on its way to becoming a timed quest without the timer showing. Those inventive Blizzard folks just keep it coming for us! 

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