The space prison, where the prisoners can play Yahtzee for the rest of their lives. It is below the event horizon slightly.
No, it isn't. It is below the event horizon significantly. If you want your prison to remain at a roughly constant distance from the central singularity, it will have to be inside a rotating and/or charged Kerr-Newman black hole, and positioned inside the inner horizon. If it's not a Kerr-Newman black hole, the prison will inevitably fall into the singularity in a very short time--a matter of hours, even for the very largest of hypermassive galactic black holes. If it's not below the inner horizon, it will inevitably fall through the inter-horizon space in a Very Short Time.
That also means that it is not possible to string a static tether between the prison and an orbiting anchor station outside the black hole. Could you build an anchor station with a tether going down to the event horizon? Possibly. The black hole would have to be rotating ridiculously quickly to put the innermost stable circular orbit at a low enough altitude to permit the construction of a cable that could reach the event horizon without breaking under its own weight, but it's not physically prohibited. And while the control systems would be ridiculously sensitive, if you can build an orbital station, you could even probably build an orbital ring which could support an arbitrary mass of tethers and prison facilities arbitrarily close to the black hole.
But the exterior anchor station will always be separated from the interior prison by the inter-horizon space. And any piece of tether that crosses the outer horizon will be inevitably transported through that space, as inevitably as it moves forwards in time, until it crosses the inner horizon. This is true even if the black hole is massive enough to make tidal effects (and therefore spaghettification) utterly negligible at the outer event horizon. Tidal effects have nothing to do with it. Bits of the tether that are below the outer event horizon are moving in a different direction through time than bits that are outside, and they cannot remain connected.
So, you cannot have a static tether. You could, maybe, continuously feed tether material down into the black hole, but what would be the point of that? In that sort of extreme environment, there is no practical difference between that, and just firing a stream of individual atoms of tether material into the black hole. It gains you nothing over just dropping an "elevator car" freely, with rockets to ensure that it can (theoretically--after all, you'll never know if it actually made it or not, once it crosses the event horizon) navigate to and dock with the prison on the other side.