The Davidson River in North Carolina is one of the top 100 trout stream in North America as per Trout Unlimited. It has fantastic year around fishing, and although the hatches are not unbelievable thick clouds of flying insects, they are steady and reliable.
The water is very clear and the fish see a lot of flies. Success will depend on your presentation 7X tippet is virtually a necessity. Try small flies Griffith Gnats and midge patterns for if it is small the fish can't be as discriminating. For nymphs use #18 Pheasant Tails or Hare's Ears.
For solitude try the winter, and you may still have to walk a bit. The beauty of this stream is worth a visit regardless of the fishing.