The New Zealand Parliament precinct sits at the top of Lambton Quay on a prominent hill, and it is worth going inside. Free guided tours of the parliamentary buildings run most days and cover the debating chamber (which can be watched from the public gallery when parliament is sitting), the history of New Zealand governance, and the distinctive Beehive — the circular executive wing designed by Basil Spence that has become the symbol of Wellington.
The debating chamber is one of the few in the world where you can watch live proceedings from close range without a ticket. When parliament is in session, just ask at reception and they will direct you to the public gallery. The exterior of the precinct — the ornate 1922 Parliament House, the modernist Beehive, and the Victorian Government Buildings across the road (entirely built from wood, the largest wooden building in the southern hemisphere) — is a tour in itself.