James Bay straddles the Ontario and Quebec border south of Hudson Bay. The nearest Nunavit territory to James Bay is about 500 miles north.
If you went to the very northern tip of Labarador, then 100 miles across the Hudson Strait would be Nunavut (Baffin Island). Not sure where the official boundary is, but if you wade into the water, you can say you were in Nunavut and nobody will argue. Then you can turn 90 degrees to the right, wade a few more feet, and say you were in Greenland, which is only 500 miles away.