My dad played the Hawaiian music that was popular in the '20s, when he started learning to play. He never gave it up; although he broadened out to many other kinds of music, I think the Hawaiian stuff was always his favourite, and when I learned to play I chorded for hours to all those old songs. Most were from Tin Pan Alley, some based on actual Hawaiian songs (I would guess). It's hard to say which are my "favourites", as I got heartily sick of most of them at the time (but I'd give anything to hear him play again -- he lost his faculties to Parkinson's Syndrome in the last years of his life).
The ones I remember most, I guess, would be "Aloha Ohe", "Little Grass Shack", "Malahini Mele", "To You, Sweetheart, Aloha", "I'd Like to See Some More of Samoa", "Hawaii Calls" (the theme song of the radio show and movie), "Beyond the Reef"... That'll do for now. I'm sure I could dredge out many more.