You might try the Big Apple Bar in New York, New York. Open 24 hours. Average drink price = $5.
Decent breakfast is more difficult. San Remo (Hooters), just off Strip on Tropicana Blvd. behind the Tropicana, did have a $5.95 prime rib and eggs with hash browns and toast available 24 hours, but with their remodeling, I don’t know if it is still available.