There is no default location for backup. In FHS 2.3 under the "Purpose" section of var, it explains why that's a bad idea to use /var/backup(s).
The proper place would be, dependent on the application and its usage, something like:
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/ is arbitrary based on the application maintainers.
Let's say that you are using rsync and that this machine is providing a backup service for the network, you would use: /srv/rsync/backups.
Folder /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. 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).
You can use next directories:
- /var/srv_backup/www - files of sites
- /var/srv_backup/db - dumps of databases of sites
- /var/srv_backup/ftp - dump of ftp server
- /var/srv_backup/svn - dump of svn