The best thing you could do is get a tour of the experimental hall where the detector is, but sadly right now you won’t be able to go down there because the machine is running and it is all closed up.
To be honest I haven’t thought about visiting from the point of view of a visitor – I am always there foe work and just go to the places I need to. There is something called the globe of innovation where they have exhibits I think. I don’t know if there are tours of the control rooms for the experiments – you could ask about that.
At first glance, CERN doesn’t *look* like a hi-tech place. It is a collection of various sheds and things built since the 1950s.