To create a public area for users to share files with the snap, you or your snap can create a 1777 tmpdir-style directory in SNAP_DATA or SNAP_COMMON.
A “private area to be shared by users of the snap” is more difficult (since it implies that non-users of the snap should not be able to write to this area), but will be made possible when Multiple users and groups in snaps is implemented. You will be able to create a group for your snap and then add any users of your snap to that group, then create a dir with 0770, 1770 or 3770 permissions with root:yourgroup ownership (you can even do this now outside of the snap without official snapd support by creating the dir, creating a group, adding users to that group, setting the root:yourgroup ownership and setting the permissions on the dir).