I have been to Cleveland Clinic in OH for care. Not with the neurologist but 2 anestesologist pain doctors and the pain day program well for a few days of it. I have mixed feelings about CC and overall was not happy with my care. I know someone not with PN but RSD who was. I think it is less the hospital and more the doctor you get. Not to say I would go to a bad place but overall.
An option you may want to ask about is sending your records for them to review before you fly out to see if they feel they can help you. I did that with Mayo. I have traveled a lot for specialists and have been let down.
In terms of who to see I would call the department such as neurology and explain a little about yourself and they can maybe refer you to whom works with this more then others.
Where do you live? I ask because my best doctor actually came from my hometown evern better then at Cleveland Clinic or UCLA etc. I had heard on here about teaching and university hospitals so I found one in my area. I did not want to see a student though. Anyhow I called the area I was looking at which was pain clinic/anestesologist and explained my condition etc and they set me up with the director who dealt a lot with the condition. You may want to look into that too.