Places in Rhode Island that are ridiculously cheap? The kind of place where you wonder how on earth they stay in business. A limited menu is fine, and ambiance matters not a whit. For Parameters, let's say Entrees six dollars or so, and under... or, two people feast on a bunch of little things for under $15 dollars. I mean dirt cheap -- but obviously with tasty eats.
If you've ever been to Evanston, IL, I'm thinking "Pita Inn"-territory. (If you haven't, trust me, and go when you can: divine Greek food, with most things costing $3 or $4.)
Arepas on North Smithfield counts. Where else?