As others point out there are lots of answers depending on your preferences, which island and day of departure. I fly out of TYS and my wife is from Maui so we go often. I prefer not to have to deal with interlining so I tend to go with DEN and ORD as connectors with non-stops and lie-flats to OGG. If I am having to interline or just going to HNL then I am a great fan of IAD-HNL. It is a long flight but IAD is a short hop for me from the other side of TN.