Fakarava and Rangiroa, atolls in French Polynesia. You'd be going during their winter/high season, which is may to october, and generally more dry and less hot than their summer season.
I would stay at Tevahine dream in Rangiroa, and probably Havaiki Pearl Farm on Fakarava, which is north pass. There's great diving on south pass as well, but the accomodations there aren't what we want. I'm fine in a non resort pension, but I do need electricity in my bungalow. If you don't care, then South pass has some pensions one of which is right by the pass.
Rangiroa also has a nice resort, the Kia Ora, but having stayed there once, we far prefer the Tevahine Dream pension, and the owner and his family are really wonderful. The resort is popular, we just prefer the feel of a small pension more. The snorkeling just out from your bungalows there is really quite good as well. And it's free.