Joel
As others have said, Auckland is somewhat lacking in courses worthy of recommendation. Titirangi would be the only one I would confidently recommend to a person with an appreciation of golf architecture. I played it just recently and have a bunch of photos that I am hoping to put on here.
In terms of fishing, north of Auckland by about 4 hours is the Bay of Islands which is home to some of the countries best big game fishing waters. It is also home to Kauri Cliffs which may appeal also. Alternatively, about 1.5-2 hrs from Auckland is the Coromandel Peninsula which is a great place for catching snapper, kawhai, kingfish, gurnard etc which are all great eating. Nothing special in the way of golf however.
I would personally suggest heading south to Hamilton in the Waikato where there are a handful of courses built alongside the river that are quite challenging and interesting. They are also very free-draining which is a big factor during the wetter months.
Grant