You could easily pick up a small box somewhere, at any host, and install something like BackupPC
BackupPC: Open Source Backup to disk
It will create snapshots of your remote servers, and provide incremental backups. And it's really quite nice once you get it going.
So, a cheap box somewhere with 2 or 4TB drives might cost $100 -- give or take a few dollars -- and you can back up whatever you like. If you look around, you can probably get a small box with dual HDD in a RAID1 mirror as well for the same price. WebhostingTalk is usually full of offers.