Nuku Hiva has a number of fine beaches, such as those at Hatiheu and Anaho, and there's a black-sand beach on the western side of Taiohae Bay. Unfortunately, they are all infested with biting no-nos (sand flies). These nearly invisible pests are particularly aggressive at dusk. If you do go swimming, try to pick a day when the wind is blowing in from offshore, and always lather up with insect repellent.
You will have a pretty good hike just walking along the shoreline of Taiohae village. For something a great deal more strenuous, climb the airport road to the top of Mount Muake for its view down over the bay.
In the old days, Marquesans got around by boat or by trails up and over the mountains. Many of these old tracks still exist. One of them begins at the Taetae Tupuna He'e Tai, just downhill from the Keikahanui Nuku Hiva Pearl Lodge, and goes for 3.5km (2 miles) into Collette Bay. The usually deserted beach over there is a fine place for a picnic, but remember to bring -- and apply! -- your insect repellent.
Marquises Rando (tel. 92.07.13 or 21.08.74; www.marquisesrando.com) provides professional guides for individuals or groups. Its prices range from 6,600CFP (US$83/£42) per person for a 2 1/2-hour hike to 12,000CFP (US$150/£76) for a 6 1/2-hour trek, including lunch and transportation to and from the trail heads.
In the 19th century, European whalers and traders brought horses to the Marquesas -- plus cattle, pigs, and goats -- which soon became wild and had a serious impact on native flora and fauna. You are unlikely to encounter a wild pig on Nuku Hiva these days, and most cattle are confined to ranches on the Toovii Plateau, but you will see horses along the roads and goats prowling the rocky mountainsides.
The strong, capable Marquesas horses are prized throughout French Polynesia, and you horse devotees will have rode their cousins on Moorea and Huahine. You can ride them here on many of the ancient trails, such as to Hakaui Valley and the Ahuii waterfall.
Up on the plateau just north of Taiohae, Patrice Tamarii of Le Ranch (tel. 92.06.35; firstname.lastname@example.org) rents horses, leads trail rides, and has 1- to 3-night horseback trips to the north shore, where you camp on beaches. Alphonse and Sabine Teikiteetini (tel. 92.01.52 or 21.24.15; email@example.com) lead half- and full-day rides; contact them for reservations and prices.