If you'll be sailing your own ship, the nearest islands are in French Polynesia, roughly to the WNW: the isolated Gambier Islands are 330 miles away, the Acteon Group of the Tuamotu Islands are 450 miles away, and Tahiti and the rest of the Society Islands are a mere 1,300 miles off. Easter Island is about the same distance in the opposite direction.
Passing freighters will likely be bound for either New Zealand or Panama.
