what is the default location for backup files of another server

There is a proper location.

There is a standard for proper filesystem structure. Its current version has been around for over a decade, which might be news to some Linux distros.

The latest version of the Filesystem Hierarchy Standard is 2.3: http://www.pathname.com/fhs/pub/fhs-2.3.html

There, under the "Purpose" section of var, it explains why that's a bad idea to use /var/backups:

Several directories are `reserved' in the sense that they must not be used arbitrarily by some new application, since they would conflict with historical and/or local practice. They are:

/var/backups
/var/cron
/var/msgs
/var/preserve

The proper place would be, dependent on the application and its usage, something like:

/var/lib/<app>/backups
/var/local/<app>/backups
/var/opt/<app>/backups

(I say "something like" because whether you use /var/lib, /var/local, or /var/opt is dependent on the application, its role within the system, and how it was installed. Also, the structure under /var/lib/<app> is arbitrary based on the application maintainers.)

By the way, since you mentioned it, /var/www is not the proper place for served web pages (again, this is news to some distro and package maintainers, but the FHS is older that many of them who clearly never have read it). Served content, and stored application data/assets for services belong under the /srv directory. I have been using the protocol method since 2005 and find it works quite well (/srv/http, /srv/ftp, /srv/git, /srv/svn, etc.).

Let's say that that you are using rsync and that this machine is providing a backup service for the network, you would use:

/srv/rsync/backups

UPDATE

Version 3.0 of FHS: https://refspecs.linuxfoundation.org/FHS_3.0/fhs/index.html

There is no default location.

I would not use any of the regular directories for this. Keep the server clean from outside backups and put those is a clear defined location.

Most likely I would use a removable disk and mount it. Something like /external_backups/ or /media/external_backups/ and inside that subdirectories with the server name and inside those compressed tar files.

/home/backup feels wrong; I would leave /home/ itself for users. If you want to do it this way I would create a user "backup" and the same setup as above.

Something like this (2x with a partition, 2x from a /home/backup/:

• /external_backups/AS400/20150101/backup.tar.gz
• /external_backups/AS400/2015_01_01.tar.gz
• /home/backup/AS400/20150101/backup.tar.gz
• /home/backup/AS400/2015_01_01.tar.gz

/var/backup is for internal usage indeed. The Debian package system keeps an older copy from the last but one dpkg run in /var/lib/dpkg/status-old. (By default:) In order to preserve the system for greater damage when a crash or filesystem corrupting occurs a daily backup is put into /var/backups when the file differs from the last copy. This is done from /etc/cron.daily/standard.

But there is no correct or wrong way to it (well, I discard the insane methods: like putting them in / or in /boot or something else as crazy as that).