According to a popular tradition, Captain Cook landed at Opaahi Reef opposite the Mormon church in Alofi. It's a scenic spot, well worth the short detour.
Two kings of Niue, Mataio Tuitonga (reigned 1876-1887) and Fataaiki (reigned 1888-1896), are buried at the royal tombs in front of the LMS Church opposite Alofi's post office. Nearby, adjoining the war memorial, are two stone backrests used by these kings.
The last king of Niue, Togia (died 1917), ceded his kingdom to Britain on April 21, 1900, just four days after the Americans annexed Eastern Samoa. He's buried in front of the church at Tuapa. If you're patient, you should be able to spot sea snakes in the clear water off Alofi's main wharf. It's fascinating to walk on the reef southwest of the wharf at low tide. Crevices, cliffs, and coral abound, and there are natural pools on the reef where you can safely swim. Beware of waves heralding the incoming tide, however. The Togalahi Sea Track across the street from the Niue Tourism Office leads down to the coast.