We learn in Eddard's first chapter in GoT that King Robert is planning to visit the Wall, one of the reasons he came North but he never does. Why? What happened to those plans?
Robert never says he's planning to visit the Wall. Eddard suggests it as a reason why Robert might have come to the North, but in fact he's there to recruit Eddard as his Hand.
The king kept his arm around Ned’s shoulder. “You must have wondered why I finally came north to Winterfell, after so long.”
Ned had his suspicions, but he did not give them voice. “For the joy of my company, surely,” he said lightly. “And there is the Wall. You need to see it, Your Grace, to walk along its battlements and talk to those who man it. The Night’s Watch is a shadow of what it once was. Benjen says—”
“No doubt I will hear what your brother says soon enough,” Robert said. “The Wall has stood for what, eight thousand years? It can keep a few days more. I have more pressing concerns. These are difficult times. I need good men about me. Men like Jon Arryn. He served as Lord of the Eyrie, as Warden of the East, as the Hand of the King. He will not be easy to replace.”
No he did not come to visit the wall. He came to make Eddard his hand and to betroth Prince Joffrey to Sansa Stark.
Wall is a forsaken place, Kings rarely visit it.
Only recorded instances of Kings who have visited the Wall during their reign are:
1. King Jaehaerys I Targaryen
2. King Stannis Baratheon
And neither of them visited the wall for pleasure of looking at it.
Jaehaerys had gone to repel a Wildling invasion1. Stannis had gone to do the same.
Plus there was nothing on the wall to attract Robert.
Whores of Wintertown and KL were better than whores of Mole Town and presumably vintage of wines were poor on the wall as well. He had more pressing concerns on his mind such as:
1. Death of Jon Arryn and its impacts: Lysa Tully fleeing with her son and the rift it caused with Tywin Lannister who was promised Wardship of Lord Robert Arryn by King Robert. The rift was deepened further when Robert made Jaime Lannister warden of the East instead of young Lord Arryn.
2. Marriage of Daenerys Targaryen with Khal Drogo
3. Possibility of a Targaryen invasion
Visiting the Cold Frozen hell just for the sake of administrative reasons seems out of character for Robert. He hated governing. He may have done it for the adventure but as all was peaceful on the wall at that time, there was not much adventure to be had. Robert wanted to get his hand quickly and return back to KL to enjoy the last treats of a fleeing summer.
1. One version says that Jaehaerys had gone there to discuss matters of urgent nature with his Warden of the North. Another tradition puts it that he went there to subdue a Wildling invasion. It is unclear which one is true. It maybe that both were true i.e. Jaehaerys going there to meet with Lord Stark and Wildlings attacking at the same time