If you've never heard of Nauru, don't feel too bad.  It's the smallest island nation in the world and it's not so easy to get to.  Flights do not come to the island as regularly as you might hope as a traveler.  From Fiji, I think there was just one flight a week.  To get there earlier, it was necessary to book a flight to Brisbane, Australia, and then head north towards the equator.

I guess it is possible to get there by boat.  Shipments of food are brought to the island every month or so.  Some people must get there by boat, but it appears that a plane is your best bet. The airport is in the Yaren community, and if you are fast, you might spot one very colorful mural on a shop right at the end of the runway.