Prisoners on death row can have visits from family or anyone on the prisoners approved visitor list.
However you usually will not be able to actually make contact with the death row prisoner like you would on a normal prisoner prison visit when you visit prisoners in less secure facilities.
I'm not sure about other prisons but there was a prison I worked at that only allowed visits to the prisoner on death row through a window.
Then you sat on one side of the window and the death row prisoner sat on the other side and you talked through a phone to them.
Now they have video visits in a lot of prisons so you may only be able to sit in a room at the prison and talk too and see the death row prisoner through the video visit monitor.