NC enjoys a fairly large swathe of highlands containing wild trout streams, including a large portion of Great Smoky Mountain National Park.  It also enjoys some of the best documented streams (along with PA, NJ, and several other states).  Be sure to check out the alternate datasets on the "NC Resources" menu, all of which can be downloaded.

Source: Eastern Brook Trout Joint Venture, Google Earth

The photo above shows one view: the brook trout habitat dataset published by the Eastern Brook Trout Joint Venture, displayed in Google Earth.  Click on the picture to see a larger image.  You can download the complete dataset in KMZ form, which can be used in your own installation of Google Earth.  The color coding in the photo is as follows, in order of best to worst:

• Blue
• Green
• Yellow
• Orange
• Red

The solid brown areas are basins where Brook Trout have been extirpated, though there may still be trout streams supporting Brown and Rainbow trout, which are more heat tolerant.  Areas which aren't coded with any color don't support any trout.  Keep in mind that brook trout can be diminished by other trout species, so some red areas may be excellent wild brown or rainbow water.  You'll certainly want to download the databases of "NC Listed WTW (wild trout waters)" and "NCDWQ Tr Water" to use alongside the EBJTV data. 

Note: these data are coded by drainage.  Not every stream within a drainage will hold trout, though the majority will, especially within the better habitat.

NC creates a very good series of county maps showing the same Wild Trout Water. as the  "Listed WTW" data (though updated more recently).  Click on "NC County Maps" in the Resources menu in the sidebar to see a preview graphic and click map.