All of Hiva Oa's hotels and pensions offer various meal plans. If available, I would opt for a rate that includes breakfast only. You will likely have lunch on an excursion or at a "snack" in town while seeing the sights, so there is little point in paying for that in advance. I also like to dine out while here, so I don't pay for dinner, either.
The most remote place to stay is Pension Peheku'a (Chez Marie-Antoinette), in Puamau village on the far northeastern shore, at least 2 1/2 hours by road away from Atuona.
Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.