I think there just isn’t a single definition that pleases all and everyone. And not every possible definition is useful in every circumstance.
For me personally, “nature” isn’t a place, but a system. Anything that adheres to the principles of that system is “part of nature”. Also, the “nature” of any thing usually tries to define the most basic principles something adheres to (e.g. “it is human nature to do […]”, or simply “it’s natural to […]”).
Often when using the word nature, however, people mean any place with no or minimal human influence. I don’t like that because it’s too black and white and it assumes that generally humans aren’t part of nature (which I don’t agree with).
I personally think that the word “wilderness” or something along those lines is more fitting for these circumstances.
Also, on a tangent: I also strongly disagree with assigning any value to the word “nature”. Just because something is natural doesn’t mean it is good. (Take a volcanic eruption or an asteroid impact, for example)