We made sure we stopped at The World Famous Coffee Cup Cafe on the way out from Vegas to the Hoover Dam over Memorial Day weekend. Kinda exactly what I pictured.
Kinda thought it would be a little more fun, though, but it was like any other diner experience. Order, eat, leave. Nothing special, really. The food was decent, the service friendly, bathrooms clean.
Probably wouldn't go back, but glad I did it at least once only because it's "World Famous".
There are some fun little shops next door. If you are looking to get out of Vegas for a few hours or are on your way to Hoover Dam, I would probably recommend stopping in for breakfast or lunch.