The Great Smoky Mountains are one of the last preserves of wild trout water in the deep south.   Below, you see the park boundary (Green) and brook trout habitat quality as rated by the EBTVJ dataset.  It's clearly the best habitat in the area.  That said, brown and rainbow trout predominate.

Source: Eastern Brook Trout Joint Venture, Google Earth

According to the NPS, there are 2,115 miles of streams in the park, but only about 800 miles hold fish, and only about 133 miles hold brook trout, all pretty much in headwaters streams above 3,000 foot elevation. Below 3,000 feet, most streams hold brown trout or rainbows that were originally introduced via stocking.  As you get lower still, below about 2,000 feet, the cold water habitat turns to "cool water", and species like smallmouth bass predominate.

Trout habitat in the Smokies is under considerable stress from a combination of acid rain and climactic warming.  Since the 1980s, 6 populations of brook trout have been lost to increased acidity.  Nevertheless, there are many streams in the park that support robust populations of wild trout.  According to the Park Service's "fisheries facts" flyer, the top streams boast fish counts in the 2,000 to 6,000 per mile range, of which around 10% will be "legal" size for harvest (i.e. >7 inches).  Most of the fish are small (under 9 inches) and fish larger than 12 inches are rare, with the exception of brown trout which turn piscivarious (they eat other fish).

There are many fishing guide books to the Park, and as we've never been there ourselves, we would not attempt to steer you to the best fishing (indeed, we never do that.  We feel it would be cheating).  However, some of the datasets you can download here might prove useful, especially if you're trying to get "off the beaten track".

Source: North Carolina Center for Geographic Information and Analysis, 20060209, Statewide 24k hydrography (lines): North Carolina Center for Geographic Information and Analysis, Raleigh, NC. Google Earth

The image above shows the NCDWQ Listed Trout Water, which of course covers only the NC portion of the park.  While we don't have any GIS data for the Tenneessee side of the park, we have provided some TN stream survey documents that might prove useful.  You'll need to slog through them, but most years there's detailed information about at least one or more wild trout streams within the park boundaries. On the NC side, listed streams are shown in Cyan.  The red lines show hiking trails.  The photo below shows a detail of the lower Hazel Valley, by way of illustrating what the dataset is like at high resolution.

Source: North Carolina Center for Geographic Information and Analysis, 20060209, Statewide 24k hydrography (lines): North Carolina Center for Geographic Information and Analysis, Raleigh, NC, USGS/NHD dataset, Google Earth

In this image, as before, the NCDWQ trout streams are shown in cyan.  The blue/grey streams show other streams within the NHD database, roughly the same streams shown on the 1:24,000 series of topographic maps.

If i were visiting the park, I would buy and study the typical fishing guides and trail maps (major trails within the park are shown in Google Earth) to decide the major drainages I wanted to explore.  I would then plan day hikes or back-packing routes, looking to fish both the major streams and their smaller tributaries based, in part, on the datasets published here.