We stumbled across this "restaurant" called Tsukenjo while driving around downtown Honolulu. It's more like a hole in the wall kinda place. Not fancy at all and only has basic amenities. However, the food is excellent and even saw a local policeman buy his lunch there. It's very affordable (around $7 to $8) and the portion is good for two people. Menu changes daily. I have photos but I cannot seem to upload them.
When you see a kau kau wagon, you can buy plate lunches there. The menu also changes daily but there is not that many options. It's also very affordable, two scoops of rice and some meat+veggies is about $5.50 (this is a medium size).
Also, there's a local chain restaurant called L & L that is worth a try! Some of the food you might find weird but it's actually really good. You may have heard of Loco Moco where you get two scoops of rice, hamburger meat covered with gravy and eggs on top. Give it a try before you decide it's not for you. The prices are affordable too, less than $10 and there are many locations. So if you're looking for a cheap place to eat, you can consider it.