It's the the Golden Steer, located at 308 W. Sahara Ave. (just west of the Strip.)
Opened in 1958, this is one of the oldest restaurants in Las Vegas and one of the few authentic joints from those old times that still exists. It's been expanded somewhat over the years from its early days as an intimate bar and restaurant, but it's still very close to what it was in its original incarnation. The Golden Steer was the subject of the February 2007 "Local Corner" in the LVA newsletter, where we noted that the food is classic steakhouse fare, but what you really go here for is the history and atmosphere: The service is classic old-school Vegas and several of the big red leather booths do indeed have brass plaques indicating that this was Frank's or Sammy's or whomever else's regular table (and we pretty much believe them).
Joints like the Golden Steer are a dying breed, so we do recommend that you pay a visit while it's still there. Not that we've heard any rumors to the contrary, but things change fast in this town and this is a place you should experience at least once, even if only to get one of the great martinis at the bar.