Hammner is just beyond my roaming area. So most of my thoughts are from what others have told me and are not from first person observations.
There are several good rivers a short distance drive away.
Upper Waiau: Never been there but it has a good reputation, requires a 2 hour walk I believe over private land. 10lb fish are suppose to be relatively common.
There is also good fishing to be had in the middle waiau, but I have never tried.
Upper Wairau: This is a river I have fished a few times, many people love it and can catch many fish a day. Would be around a 30-40 minute drive. The rainbow river is also worth a look. Good numbers of fish and a real possibility of a few big ones. The wild gooseberries should be ripe but their location is a secret because I plan on raiding them shortly.
The tarns of Tarnsdale are also little gems. I like Fish lake (relatively short walk) but I know someone who works with DOC up there and he claims that trout are easiest to spot in bowscale. They are quite plentiful, but it does get windy.
Clarence: Quite a scenic looking river, every time I driven pass it is being heavily fished. One time I drove around three corners in a road and saw three different people parked and fishing..... It does hold fish but it does get thrashed over the holidays.
The rivers in Molesworth are highly scenic, but never fished them. I plan to one day. They are worth a visit for the scenery alone and I believe the fishing can be productive but the going is hard. There is a large gooseberry patch at the accommodation house campground just before the start of molesworth. They should be ripe and tasty. They are even growing high up the side of the hills in damp spots.
Lake Tennyson is a option, plus there is a secret patch of gooseberries hidden at the side of the lake.... I do not believe the fishing is that good.
If you are prepared to drive over the Lewis pass, then you would have access to the Maruia. This river holds a impressive number of trout. I have seen the most fish below the spring junction but above the waterfall. River access can be tricky. The best fishing is in the gorge section but it is a large day to walk through... really requires two days to fish.
So I really only have first hand experience fishing the Tarns, Upper Wairau/Rainbow and the Maruia. I spent a evening spinfishing in the clarence but that does not count.