By definition a disaster recovery solution needs to be geographically separate. You're protecting yourself from catastrophe, and some of those scenarios include your main location burning down, flooding, being hit by a tornado, etc etc.

So you either need to collocate systems with a friend who you trust, purchase colocation services from a provider, or use a cloud service to achieve what you're looking for to truly have a DR solution.

As far as how to do that, the main idea is to have that point in time available on a system that, even if you get compromised, the backups won't. The old school method here is to use an external hard drive or a tape device, and physically store that offsite. So like use your regular backup mechanism, and in addition to what it's doing now schedule a daily/weekly/monthly job that backs up to this other device, and then store that away from your main location.

That's essentially the idea though, and there are any number of solutions you can use to do it.