Most streams in the park hold trout unless they are just very small or tiny streams. Not a lot of trout down in lower abrams creek below cs 17 but even a few there. Just read back through the posts on this blog and you will find many suggestions. The little river above Elkmont is a good standard one that is hard to go wrong on. Also the other usual spots Deep Creek, West Prong of Little Pigeon, West Prong of the Little River, Middle Prong of the Little River (along Tremont road) etc. Those are some of the big ones with fairly easy access but there are many more.
A real good place to get a better answer is Fred Turner's site (smokystreams.com):
He has a lot of maps on there that will show you all the streams with trout and even breaks it down by species.