Nugget Diner
There's a small casino on Virgina Street downtown accross from Harrah's called the Nugget. There's a small diner in the back that's very cheap. It's not for everyone - definitely on the shabby side - but the food is actually not half bad.
A small step-up would the coffee shop at the Cal-Neva. Also decent food at good prices. A little nicer and a little more expensive than the Nugget.
If you're going to be heading away from downtown, the coffee shop at the Peppermill is excellent, a legitimately nice place that has some very good "comfort food" specials for $5/95 Monday through Friday.