"what command can be used on most linux distributions to find the directories where the man pages are kept"

Base name or -b command is used to locate only match directory in Linux.

Explanation:

base name can   primarily be used in shell script.

As we know that base name can be described  as a standard UNIX computer program. When we give a path name to any base then it  deletes each and every  prefix up to the last slash character and give back the result. base name can be defined in the Single UNIX Specification