I can't think of anyplace more secure than the galactic core. Nobody in their right mind would want to go there, and even if they did as we have seen only a ship with the Reaper IFF can survive the journey.
One could argue that the best kind of security is obscurity. If the Collectors had Reaper drives then all they would need to do to ensure complete privacy is to pick a random point 100 hours travel beyond any region of space with gas giants, and build their base there. This could be either beyond the galactic rim, above or below the disc, or perhaps in a low density region within the disc such as the relative voids between the spiral arms (forgive me if this isn't the case, I'm assuming those are empty but I'm not an astronomer). With nothing to discharge onto, none of the council ships would be physically capable of following them even if they knew where to look. That is, after all, the strategy that the Reapers themselves use out in darkspace.
The Omega Relay, by contrast, is a very conspicuous locked door. And it's a sad truth that if you go to the trouble of locking a door, some nosy so-and-so will wonder what was worth locking away and try to find a way in to steal it. As, indeed, Cerberus eventually did.
Edit: I'll admit though, that supermassive black hole did make for one hell of a cool backdrop.