New Zealand’s larger cities have extensive bus services but, with a few honourable exceptions, they are mainly daytime, weekday operations; weekend services can be infrequent or nonexistent. Negotiating inner-city Auckland is made easier by Link buses; Hamilton has a free city-centre loop bus; Christchurch has city buses and the historic tramway. Most main cities have late-night buses for boozy Friday and Saturday nights. Don't expect local bus services in more remote areas.
The only cities with decent local train services are Auckland and Wellington, with four and five suburban routes respectively.
The main cities have plenty of taxis and even small towns may have a local service. Taxis are metered, and are generally reliable and trustworthy.
Hitchhiking is never entirely safe, and we don’t recommend it. Travellers who hitch should understand that they are taking a small but potentially serious risk. That said, it’s not unusual to see hitchhikers along NZ country roads.
Alternatively, check hostel noticeboards for ride-share opportunities.