We did the cruiseline sponsored Wellington Highlights excursion. There is a shuttle available from the ship for $6usd each way. Tickets could be purchased on board charged to your SeaPass. It's a 10 min drive, so might be too far to walk.
On our excursion we stopped at the botanical gardens, the cable car, Mt. Victoria,Old St. Paul's Church,the waterfront, Parliament House and the "Beehive", another distinctive government building. We drove all around the city with our hilarious bus driver--he should have his own show, lol.
Except for Hobart and Wellington, all our excursions were day-long and included lunch.
When are you going and what ship?