Where in Hawaii is it tropically beautiful, the beach perfect, mountains in the background, few people?

It's going to be quite difficult for you to find a place with "no tourists, just a few locals". Your best bet, I think, would be to do a web search for bed & breakfasts in Hawaii. On Oahu, communities like Kaaawa, Hauula, Mokule'ia & Haleiwa might work. Kailua has lots of B&Bs, but would be too crowded for your description. Neighbor islands will be considerably less crowded.