Go there and select location strip and other late-night. Click on the individual restaurant to see if it's 24 hours or just open late. A couple of decent 24 hour ones are Peppermill and Grand Lux.
First ones that come to mind are some of the hotel cafes: Cafe Bellagio, TI coffee shop, Paris (Ile St. Louis?) & Monte Carlo coffee shop, also Carnegie Deli at the Mirage and Grand Lux at Venetian.