Welcome to Just Answer and thanks for your question. A teaching hospital is a great idea, but I would switch to a gastroenterologist for your reflux. Any teaching hospital in any state would be fine. There you will find the latest in treatment, including an interdisciplinary approach. In addition to Nexium, you can also try another over-the-counter medication called Gaviscon that contains alginatec which coats the esophagus and really helps with the pain from acid reflux.
Yes, a gastroenterologist treats all of the digestive system from one end to the other. He or she would be the real expert in reflux. In New York, I would go to Mount Sinai or New York Presbyterian. We don't recommend specific doctors, but you will find a number of them at both medical centers.