Where should you store your Joomla backup files? Actually,  there is no single best answer because you should keep copies of your backup files on multiple locations. 

However, the following should work well in the most cases: 

1) Store more frequent copies with an external hosting provider. For example, if your current hosting provider has a major issue (fire, earthquake, system compromise...) from which they could not recover, you would be able to recreate your website with another hosting provider based on your backups stored there.

2) Store less frequent copies locally on your external hard drive. For example, if everything fails, you would still have most of your data preserved. While making local backups may be inconvenient  due to lower Internet connection speed or automation issues, it is an important aspect of your Joomla website backup mix. 

Check with your Joomla developer where you website is hosted and make sure you're not the next horror story I will hear about.

Ogy Nikolic
Joomla Consultant