Star Noodle, Mama's Fish House, Aloha Mixed Plate were all among our favorites on a recent trip. Star Noodle as a James Beard semifinalist, and as such I think it is often surprisingly difficult to get a table. For breakfast we liked the food and loved the scenery and atmosphere of the Gazebo which is fairly close. There's always a wait, though. Their mac nut pancakes are the BEST we had in Hawaii. Da Kitchen is great too, but we never got to try the one in the wharf so I can't vouch for that one (we tried the one near the airport)
A lot of people like Honokawai Okazuya for plate lunch; I found it a bit overrated but did really enjoy the sweet chili salmon.
Ululani's (near Kimo's, etc. on the main drag) has the best shave ice I've had on any Hawaiian island.