The NYS Department of Enviromental Conservation, Division of Water, Bureau of Water Assessment and Management publishes a massive dataset which categorizes the water quality of most streams in the state.  Though the dataset is incomplete, where it exists, it is clearly one of the most useful available.

Of relevance to us, many streams are categorized as either "T" (streams that support trout) or "TS" (streams that support trout spawning).  In the photo below, you see the entire dataset.  T waters are coded blue; TS waters are cyan.  The water quality data is shown on top of the EBTJV basin data, which codes the quality of brook trout habitat.

Source: NYS Department of Enviromental Conservation, Division of Water, Bureau of Water Assessment and Management, Eastern Brook Trout Joint Venture, Google Earth

You can download both of these data sets from the NY Resources menu on the right.  You can also download a tutorial on how to set up your own "Wild Trout Workstation" for free from the Google Earth page in the GIS Tools menu.

The NY Water Quality datasets are clearly incomplete.  There are no T or TS streams at all in the finger lakes region.  As well, there are virtually no streams coded as "TS" in the northeastern quadrant of the state, despite having some of the best habitat in the state.  So, best as i can infer, streams which are coded TS are clearly wild trout streams, while streams coded T might be wild trout streams.

Because the tool I use to create KMLs limits me to a maximum input dataset of 10MB, the streams are divided into 31 files:  two files for each of the 17 "major basins" in the state (less the basin in the center of the state which is empty, and one other basin which has only T streams and no TS streams coded).  You can download the entire package in a single Zip file of 30MB.

Note that the files default to a "blue" stream color.  You can right click on the TS streams and change the color to something else (I chose Cyan here).