Wellington is the capital of New Zealand.
When arriving to Wellington, you might be able to catch a local train, but even at night it's worth to just try to hitchhike into the city when you're North from the point where the highway starts.
Heading North[]
Ferry to South Island, Picton[]
You can't take the ferry for free. Guaka hasn't tried hitching a ride from cars going on the ferry, but apparently you pay per person. And it's better to book in advance. (They even have some kind of limit of people they let on the boat.)
If you ask around a bit on the ferry it will be easy to get a ride to Nelson or other places in South Island though.