You can probably skip
/var/run, but that directory holds so little data, it's probably not worth skipping.
Sure, you can back up to
/var/backup (or whatever location you wish, really). Just be careful exclude your
/var/backup from your backup sets otherwise you'll get into a recursive backup situation, which isn't good.
Additionally, I assume that
/var/backup is on local disk? If so, make sure to consider how you'll get the contents of
/var/backup off of local disk to a remote location somehow. Needless to say, those backups won't do you a bit of good on local disk if you have a hard drive failure or filesystem corruption.