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TripGo: https://play.google.com/store/apps/details?id=com.buzzhives.android.tripplanner&hl=en_US
It’s not google maps, but oh man does it do what you need well, it’ll combine bike and transit, Uber and transit, park and drive m, and all other stuff. Not available everywhere, but chances are it’ll work.
Transit works well. Another app to try is called TripGo iOS Android
This website also has good travel info for Wellington, Auckland and Christchurch https://waka.app/ - Just use the change city option to choose Wellington. You can also pin the web site to your home screen.
There are also these apps Bus++ Wellington and Wellington Trains
Google Maps has public transport info as well.