Where can I publish failed research directions?
I think that one has to distinguish different kinds of failures, and also see if the field is experimental or not.

If you have done experiments and they show that some approach does not work, it is perfectly fine to publish that (although, as is discussed in various places, you often do not get the credit that you deserve for this).

If your work is theoretical, it is important that you can formalize the "dead ends" in a sufficient useful way; for example by proving that objects of a certain kind or with certain properties do not exist or that an (intuitive) lemma is wrong which can be shown by a counterexample.