Where should an Ubuntu admininstrator (user) mount directories not established by the distribution?

It appears (largely through observation) that ubuntu performs automounts into /media/{administrator/user} (if true, better than /mnt)

• /mnt used to be for fixed disks (hdd, sdd) but it is discarded nowadays in favor for user defined partitions (ie a mountpoint in /).
• /media for removable media (cd, dvd, bd, usb)

/srv if not used by ubuntu

Not by default; it is for services to use and those you install as extra software. /srv has a couple of note in the FHS:

One method for structuring data under /srv is by protocol, eg. ftp, rsync, www, and cvs

Data that is only of interest to a specific user should go in that users' home directory. If the directory and file structure of the data is not exposed to consumers, it should go in /var/lib.

So the use case for the directory is limited as it as.

A couple of examples: cgi scripts, ftp downloads and such.

Now I want to create directories on a user data for a file server, user media for a media center, directory for source control, etc. Many of these directories will be on devices other than the boot device

You can use /srv/ for that. The idea is to create a sub directory based on protocol in there.

I would use a different disk or partition for this though and create a new directory in / specifically for this that is used as a mount point with a name you make up. 100% guaranteed no default is going to touch that mount point (Ubuntu/Linux will stick as close to the FHS layout)