I use to live in Koloa and Poipu and do drive over to the southshore periodically.  Poipu and the adjoining coastline has turned into a tourist destination so you won't find "plate lunch" places.  If you go into Koloa you'll find two ono (tasty) cheap eats ... Koloa Fish Market and a snack shop along side of Sueoka Store.   There are many other so called local places and I use to frequent Lihue Cafe for lunch before I was placed on a diet.  I still cheat and love their roasted pork plate on Wednesdays ... loads of chunk pieces of pork over white rice smothered with brown gravy and fresh green salad with a soy sauce dressing (or macaroni salad).  Yeap, high fat and sodium but so ono.  Enough food for three normal sized people or one of me   .  Then there is alway the infamous Hamura Saimin stand in Lihue on Kress Street.