How can I recreate a directory structure, without the files?

Probably, the most easy to understand one, and the second "find" line does the same with files, creating their "dummy" copies, being empty, but having the original's modification and access times:

With the cpio program:

or with GNU tar, and more verbose syntax:

This creates a list of directory names with find, non-recursively adds just the directories to an archive, and pipes it to a second tar instance to extract it at the target location.