.NET URI: How can I change ONE part of a URI?

You can use an UriBuilder to modify individual parts of an Uri:

Uri uri = new Uri("http://stackoverflow.com/questions/2163191/");

UriBuilder builder = new UriBuilder(uri);
builder.Host += ".nyud.net";

Uri result = builder.Uri;
// result is "http://stackoverflow.com.nyud.net/questions/2163191/"