In Lihue I'd say Hamura Saimin and Duke's for lunch or Aloha Hour. If you are in a condo at the Marriott, maybe get the Pau Hana special from Mark's Place or to go from Garden Island BBQ (Chinese). Dani's and Tip Top are great for breakfast.
If you get down to Poipu you have Merriman's, Roy's and Tortilla Republic, a great upscale Mexican restaurant.
Near Waikoloa I'd look into the Merriman's there as well, Hawaiian Style Cafe for breakfast, Roy's in Waikoloa, Brown's Beach House, Canoe House, especially on Thanksgiving Day if you are on the BI and the Mauna Kea Clambake if you are on the BI on a Saturday.
Rapa nui island cafe in Kona is fantastic. It's a hole in the wall and hidden, but totally worth it. Go for dinner,,,get the Thunder steak, shrimp stir fry with macadamia nuts, veggies, peanut sauce and the house rice with coconut. Yum! So good we went there twice.
It might be a drive depending on where you're staying, but Mi's italian food is also very good...make a reservation.
Not a lot of standouts in terms of dessert. Go to Target, buy a half gallon of Roselani Haupia coconut ice cream and indulge in a bowl each night. Heavenly.