Typically the reactor control systems are either going to be old PDP and System/360 boxes or just tiny purpose-built clusters of transistors and logic chips. Its rare to see a Nuke plant with TCP/IP running, let alone anything even remotely connected to the internet.
Some plants will have regular desktops scattered about for use by the Reactor Control staff, but those don't do anything all that important and are usually there for recreation and communicating between staff and sometimes between the plant and the utility operators.
But even if the plants get hacked, the technicians are still there monitoring everything via mechanical gauges and have the ability to switch over to purely manual control.