All of the cheap restaurants, known as warungs in kuta are probably the cheapest you will find in any touristy area.
Warung Indonesia is the best and cheapest for local Indonesian food. Instead of ordering off the menu, go up to the counter with all the food on display and pick out different sides you want.
Warung Slouvaki is the best Greek food you will get outside of Greece. Get the chicken pita souvlaki. It is right down the street from Warung Indonesia.
Nebula is opened all day long but it is the best for breakfast in Kuta.
Mojos is a really small hole in the wall Mexican joint that you can get very affordable authentic Mexican food.
Balcony has all different kinds of Western and Asian food. Try the Tuna tataki.
Sky Garden buffet is every night from 5-9. It costs about $8 for all you can eat AND drink.
At Swich you can make your own sandwiches. They have tons of different bread and toppings to choose from. They also have vegan and vegetarian options.