Today I went to Karamatura forest park in the Waitakere ranges, just past Huia and there are streams galore in there. Many are fast flowing but along the loop walk there are tiny pockets of water that has come from up the hill - I saw what looked like a tiny spider on top of the water, too small and not enough light to get a good look though.
Very nice to place to go for a walk - I can't vouch that there are critters to be caught but I would certainly think there would be. An experienced fisher would know which rocks to look under
If you haven't been, head for Titirangi Village, then at the Sculpture roundabout take Huia Rd and follow it till you get to the Historic museum. Past Woodlands Park and Laingholm, just before the museum on the opposite side of the road is the entrance to the park.