When I plug in a USB stick the system mounts it to a directory under /run. Is there some way I can change that to have it mounted under a different directory?
Thanks in advance.
Make an /etc/fstab entry for it. Of course you must then identify this mass-storage device in a unique way. Thus use one of the /dev/disk/by-* symbolic links.
When there is an /etc/fstab entry, the automatic mounting by the desktop will not take place. Thus mounting must be done either by root directly, or indirectly by the user which requires the usage of mount option user.
Of course see
man 8 mount