Because of these factors, it would behoove your government to give close consideration to this issue and take a pro-active stance. It would be nice to see Nauru gain a long term benefit from this resource, rather than have it become an exploited Panama, or as in your not so distant past, a wholesale rape of your island by mining speculators.
Could the unproductive land in the island interior be nationalized? If that were possible, it could be leased to the highest bidder without the conflict that would inevitably occur if it were left to real estate speculators.
When you have your ducks in order, it would be prudent to start making NASA, the European Space Agency and the Chinese Space agency aware of your real estate. As far as the media goes, this will be a very "sexy" issue, and your nation is sure to gain a lot of coverage, long before the space elevator is actually realized.