Maupiti's pretty low-key and you can really explore it on your own, by bike, or by foot. Pensions will organize a half-day or full-day excursion on the lagoon, which can cost from 2,500 to 5,000 CFP depending on whether a picnic is included.
Tereia Beach is the main island's only beach and it's on the western side of the island. It's often completely deserted and there are no shops. You can even walk across the lagoon at low tide to Motu Auira. The best beaches are on Motu Auira, to the west of Maupiti, and Motu Tuanai, to the east. They are long and white, with crushed coral in the sand. Beaches line the azure blue lagoon and make for classic island paradise vistas with palm trees bending towards the water, while it's only a short walk from the lagoon to the ocean on most motus so there's really two beaches—the calm one and the ocean beach with waves. In the low season (February to May) you may have long stretches of sand to yourself.
Some of the island's marae date to the 9th century. The Marauira marae is on the west coast and Vaiahu marae is on the south. Ancient graves are located on Motu Pae'ao in the north, and turtle petroglyphs are on the north side of the main island. The petroglyphs are often hard to find; ask the pension owner or someone in main village for help.
Hina's Tiare, the little flower known as the moon goddess in Tahitian, grows only on Maupiti and Motu Pitiahe in the south.