The city that never sleeps can’t have too many 24-hour diners. Long Island City’s Court Square Diner (only three subway stops from Grand Central) is popular with Queens and Midtown chowhounds alike. Its recession-proof prices can’t be beaten, and free delivery in Queens helps, too. Diners flock here for hearty greasy-spoon staples like charbroiled burgers and disco fries, served with melted cheese and gravy.