For anyone staying up here, this is the useful list — what is actually worth giving up a North Shore day for, with the booking traps attached.
Pearl Harbor, about 50 minutes down the H-2 and H-1. The USS Arizona Memorial programme is free but requires a reserved timed ticket booked in advance through recreation.gov, and they go quickly. There is a strict no-bags policy with a paid storage facility on site — turning up with a rucksack is the standard mistake. Allow half a day minimum.
Diamond Head, about an hour and ten. Out-of-state visitors must reserve entry and parking in advance; you cannot simply drive up. It is a short, hot, busy walk with a good view, and it is a long way to come from Haleʻiwa for it.
Byōdō-In Temple, Valley of the Temples at Kāneʻohe, about 35 minutes down the windward coast. A 1968 replica of a Japanese temple at the foot of the Koʻolau wall, with a small admission charge, koi ponds and a bell you may ring. It is on the windward route, so it costs almost nothing in detour.
Kualoa Ranch, about an hour down the coast — film valley, UTV tours and an ancient fishpond. Book ahead; the off-road tours sell out days in advance.
Honolulu, an hour. The Bishop Museum, the Honolulu Museum of Art, ʻIolani Palace, Chinatown and the only restaurant scene on the island that runs past nine o'clock. If you are up here for a week, one Honolulu day is worth it.
What is not worth the drive from here: Hanauma Bay, at the far southeast corner, roughly ninety minutes each way with a reservation system and a closed day each week. Lovely, and there is better snorkelling at Shark's Cove in summer, fifteen minutes from Waimea.