Four days in Honolulu: a kingdom's capital that happens to have a beach attached

The flight will have taken most of a day whichever direction you came from, so the first afternoon is the beach and nothing else.

Kuhio Beach is the middle of Waikiki and the calmest part of it, because a low retaining wall offshore flattens the water into something like a lagoon. It is where beginners take their first surf lesson, and an hour with an instructor here is the single best-value thing in Waikiki. On the promenade behind it is the statue of Duke Kahanamoku, the Olympic swimmer who took surfing to Australia and California, with fresh leis on it most days, and four upright stones beside him that predate all of this and are treated as sacred.

Walk east along the sand for ten minutes and it thins out. Queens Surf is the quieter end, with better snorkelling straight off the beach, shade under the trees and a good deal less noise.

Stay for sunset, which happens directly down the beach with Diamond Head on your left, and then eat somewhere that is not in a hotel.

West today, and it is a heavy morning. Go early: the site opens at seven and the car park fills.

The USS Arizona Memorial is a white structure straddling the sunken hull of the battleship, reached by a short navy boat trip. The Arizona was hit in the forward magazine, sank in nine minutes, and 1,177 of her crew died with her, most of them still aboard. Oil still rises from the wreck at a steady drip and spreads on the surface, which people call the black tears. The room at the far end is a marble wall of names. The programme includes a documentary before the boat and takes about seventy-five minutes.

The aviation museum is on Ford Island, in two hangars that were strafed in the attack and still carry bullet holes in the glass. It holds both American and Japanese aircraft from the war, including a Zero recovered from a Pacific island, and it is the best of the several ticketed attractions at the harbour.

In the afternoon, drive back through the city and up into Punchbowl, an extinct crater above downtown holding the National Memorial Cemetery of the Pacific. Over thirty-eight thousand service personnel are buried here, from the Pacific war, Korea and Vietnam, in flat markers on an enormous lawn inside the crater walls. The lookout at the far end gives you the whole city and the harbour you were standing in that morning.

The best day of the four, and the earliest start. Both of the morning stops need reservations booked days in advance, so get those first and build around them.

Diamond Head is a tuff cone at the eastern end of Waikiki, formed in a single violent eruption a few hundred thousand years ago, and the trail goes in through a tunnel and up the inside of the crater wall. It is three quarters of a mile up with switchbacks, stairs and an old military tunnel near the top, and it takes about forty-five minutes each way. From the observation post on the rim you get the whole southern coast. Go at opening, before the heat and the crowds.

Hanauma Bay is fifteen minutes further east, a bay formed inside another collapsed crater and now a nature preserve with a hard cap on daily numbers, a mandatory briefing film and a closure two days a week to let the reef recover. The snorkelling is exceptional and the rules are strict: stay off the coral, keep away from the turtles, and use only the sunscreen sold on the island.

Then keep driving round the point. The beaches round the point are the wild side of Oahu: no hotels, lava rock, and surf that is genuinely dangerous for anybody who is not a strong swimmer. Do not go in unless a lifeguard tells you it is fine. Stand on the sand instead and watch the bodysurfers, which is the entertainment.

The drive back over the pali, or come round the windward side for the long way home.

The last day is downtown, which is where the history that most visitors never see is kept.

'Iolani Palace was built in 1882 for King Kalakaua and is the only building in the United States put up as a residence for a reigning monarch. It had electric light and telephones before the White House did. After the overthrow in 1893, Queen Liliuokalani was tried in her own throne room and then imprisoned for eight months in an upstairs bedroom, where she sewed a quilt that is still in the house. The guided tour is the one to take; the self-guided version misses most of that.

The Bishop Museum is three miles north and is the great collection of Polynesia: feather cloaks made from hundreds of thousands of birds, the royal regalia, a full sperm whale hanging in a three-storey koa-panelled hall from 1889, and a planetarium that teaches the star navigation the first voyagers used to find these islands. Give it three hours.

Then the airport, twenty-five minutes west, or an inter-island flight to whichever of the other islands you have decided to come back for.