Siroktabe Archipelago -- Indonesia
Size of your new kingdom: 0.4sqmi
Nearest humans: 3.7mi
Isolation level: Very high
Highlights: White, sandy beaches, beautiful coral reefs, and lush, almost inhospitable jungles. You can choose to island-hop by boat with a guide who's charged with catching you fresh fish, or forgo the guide altogether and fend for yourself.
How nuts? 5/5 coconuts, if you choose to go it alone. There's no electricity, no fresh water, and no chance your fire-starting skills are as good as they were back in the '92 Scout Jamboree.