OK, if you drive south on the main road out of town (toward south point & volcanoes) there is (was) a small place on your right that serves kalua pork and lau lau - to go only. I used to have the mile marker noted down somewhere, but will never be able to find it now that I want it. Maybe about 7 miles out of town?
Then, for poke, I like the grocery store at the crossroads near Hilo (I know, I know, it's on the other side of the island). Had to check Google maps here - the grocery store is in Kea'au. They have several different types of poke and sashimi.
Or, you can just ask the locals, as my info is hopelessly out-of-date. I found some killer saimin on the recommendation of a ranger at Puuhonua O' Honaunau.