I think the term secret places is a bit of a misnomer. I've had servers from various times that I used for my own purposes, such as being essentially an anonymous FTP site that didn't have actual DNS names, so you have to know the IP to get to them. It's not really 'secret' as such, but is more 'security through obscurity' than anything else. Much of the 'dark web' is like that. You get to a system by IP rather than name. Trouble with that though, is that anyone can scan IP address ranges looking for web servers, and plenty of people do, as I can tell from my access logs. Because of the way the internet is designed, it's difficult to actually hide, though you can do things like use non-standard ports which will keep you off the radar for the most part, but even that doesn't help against portscanners. To really hide, you need 'port knockers', but only the more sophisticated can get away with that, because it really does make it difficult to connect to without specific scripts to do so.
All of the above being said, it is fairly easy to hide under the radar for some values of 'hiding'. Anything you want to have external folk connect to though, isn't really going to be able to get very stealthy, just because of the way things work.
It will be interesting to see if the widespread implementation of IPv6 will make things 'better' from a hiding standpoint. There will certainly be a lot more address space to scan. Of course, I'm not really holding my breath for what I'd consider to be widespread implementation of IPv6.
We use IPv6 at the University but we also have Internet 2. There’s a lot to be said for downloading Linux distros in just a few minutes.