In the books
In the A Song of Ice and Fire novels, Old Wyk was the first of the islands to be settled (despite being located on the far side of the archipelago from the mainland), and the ironborn still hold it to be sacred.
It isn't as large or wealthy as Great Wyk, Harlaw, Orkmont, or Pyke, but its "holy" status still gives it high esteem among the ironborn. Its local Houses take pride in this and are fiercely devoted raiders.
Old Wyk is the location of Nagga's Bones, a holy site to the ironborn who claim that it is the skeletal remains of Nagga the Sea Dragon, slain by the legendary Grey King in the Dawn Age. The World of Ice and Fire sourcebook (2014) confirms that they at indeed the bones of some massive, ancient sea creature - though whether they are from a mythical "sea dragon" or some kind of whale is unknown. Whatever the case, Nagga's Bones are where the Drowned Men priests traditionally held the Kingsmoot.
After Balon Greyjoy's death in the novels, therefore, the new Kingsmoot is held on Old Wyk at Nagga's Bones. The TV series cut this for time, so apparently the gathering is just held on the coast of Pyke. Concept art for Season 6, however, actually does contain an early sketch for Nagga's Bones: apparently there were originally some tentative plans to include it but they were later abandoned.