I know you said fishy and animal related but you might like to broaden your horizons with some of the following...
Petz N All is the petshop in Nelson. It recently moved. Used to be in Montgomery Square but is now in a street behind I think (head towards The Warehouse and you should see it). Sorry I don't know the address.
Founders Park is interesting. It is a ye olde Nelson replica historic village type park. Has a large pond in it. They once emptied and killed hundreds of huge goldfish that people had let loose in it.
WOW (World of Wearable Art) is great and not just for those who like fashion. Also has a large classic car collection there. Has a pond at the entrance (no fish)
I second Mapua Aquarium and the Smokehouse as good destinations!
There is an Eel Walk apparently as part of the Nelson Hertitage Walk. An easy walk around the central city. Starts at Aratuna (pathway of the eels) Normandy Bridge.
Go to the Saturday Market, 9am - 1pm, in the Montgomery carpark (behind the main street)
Tahunanui Beach is nice.
Walk along the boulder bank.
Visit the Miyazu Japanese Garden (on your left as you enter Nelson from Blenheim end)
Isel House stately home and Park
Broadgreen Historic House
The Cathedral
plenty of galleries and museums
South Street. This is Nelson’s most well known and loved historic precinct, surviving as a unique group of cottages showing everyday housing from the 1860s up until the end of the 19th century. The South Street Gallery, on the corner, was a builder’s business in its early days. The two-storeyed building on the other corner was built by the City of Nelson Civic Trust in 1999.
Off Nile Street West, South Street captures the feel of a past era. The 16 working-class cottages built between 1863 and 1867 remain intact and are still lived in. South Street Gallery sells works by several Nelson potters.