The Cook Islands
Rarotonga, the Cook Islands capital, is tiny. We're talking 26 square miles, and it's still the largest of the 14 islands that make up the Cooks.
Ironically was not actually visited by Cook himself when the good captain poked about the chain's Southern Group of islands in the 1770s. In fact, the first European to set foot here, in 1790, was apparently Fletcher Christian, fresh from his mutiny and looking for a place where he and his fellow Bounty crewmen could enter early retirement.
The culture here is Polynesian, but the local lingo is English (well, that alongside a dialect of Maori) and the currency is the New Zealand dollar. (Be wary of Cook Island dollars in circulation; on the islands they are worth the same amount as kiwi bucks, but are utterly worthless once you leave.)
This place is about as pristine as a well-known South Pacific island can be. Tourists didn't start trickling in until 1974, and it took another three years before a resort reared it ugly mass tourism head. TV didn't invade until 1990.
It's still one of the best places to get a handle on Polynesian culture, and offers fine nature hikes, excellent swimming snorkeling and diving, and some of the best fishing on the planet.
It’s also an inexpensive place to hang your hat for a while, with hotels as cheap as $30 per double, and full meals for under $15.