Our resort on a private motu runs a free shuttle boat to the village (same motu as the airport) of Tuherahera, pop. 500, four times a day.
Tips:
– you can ask for a free bicycle rental at reception, and they’ll load it onto the shuttle boat for you
– ask reception for a village map (not critical, as it is small)
– hit the store before returning, not on arrival
– bottled water is 1/6th the price compared to the hotel
– there is a bakery near the boat dock
We missed the bicycle opportunity (we had read that pensions in the village provide them, but it hadn’t occurred to us that an island resort would have them). Apparently there is a nice sandy beach on the ocean side of the motu, and a dirt road to cycle on…
So we walked around in the heat, taking one of two parallel roads to the west end of the motu where there was a nice soft coral beach and we met that fisherman with the dogs and circling sharks.
We passed an elementary school, several churches, two snack bars, and friendly locals who waved or said ia ora na (hello; sounds like yora-na)
On the way back, we stopped at the little grocery store which had more mosquitoes than produce 
We picked up cold drinks, and a few larger water bottles to take back to the hotel.
Funny story: we were at reception (next to the boat dock) booking our lagoon excursion and fancy massage) when I look around to check the time and notice the boat has already left (early). Not sure how we missed the commotion, oops. The receptionist tried to radio the captain unsuccessfully, however she did arrange for the captain to ferry us over as soon as he returned (it’s only a 7 minute ride each way).
The massage ended up being outside on a massage bed standing in the water near shore, which felt nice with the sound of the ocean, refreshing breeze, a brief rain shower, then late afternoon sun.