I have caught Brown Trout, Rainbow Trout, Brook Char and Chinook Salmon.
Have gotten Browns and Rainbows both fly fishing and spin. Only caught brooks fly fishing and my one and only Salmon was my first good size freshwater fish, before then I only caught a few yearling searuns and a skinny brown.
These really only one spot in the South Island (and maybe even NZ) where decent size brooks can be caught (there are small ones in many headwaters). Do a little investigation, you would find its name sooner rather then later. Or another more helpful poster might let you know.
Yeah, I was already aware of Lake Emily, however iv heard stories of other places, only other lake to come to mind is Hawea, but the brookies hang out in the small creeks and rivers feeding into Hawea.