Oki's Diner in Lihue - For an affordable breakfast, visit this local favorite.  Their macadamia pancakes are delicious and the unique syrup assortments are the best!  Service is a little slow, but hey, you're on vacation....and this is the islands, life is a little more laid back.  Your wait will be worthwhile!

Lihue Barbeque Inn has been around for a long time and is still a popular, local hangout. You can get a famous "plate lunch" there, fish sandwiches, ribs and more. The link will take you to TripAdvisor's listing where you can read detailed reviews from other travelers. 

Fish Express, is located in Lihue across from Walmart in a grey building.  The Fish Express name is in black paint on a black background and can be missed.  This is a great take away place.  The fish is extremely fresh.  They have a great lunch menu and a wide selection of ahi poke.  Great soft shell crab salas special!  The spicy ahi poke is the best.  Expect to pay about $6 for a plate lunch.  You can also buy seafood to prepare yourself.   

KCL BBQ in Lihue (they also have a location in Kapa'a) is a great place to get really good local food for under $10/pp.  It's definitely family-friendly.  It's located directly across the street from McDonalds in Lihue.  They have mini and regular sized portions, plus a significant ala carte menu.  The chicken katsu is the best!

You can also find some more great ideas in TripAdvisor's Lihue Restuarants listing.