The short answer is: not many, and they've been falling like flies in recent years, with the closure of the Sahara, Cappozzoli's restaurant now transformed into Flavor Flav's fried chicken joint, and the demise downtown of White Cross Drugs and Atomic Liquor, the latter until very recently holding the lifelong record Las Vegas' oldest bar (there's hope for an Atomic reopening, but not anytime soon).
So, your options have been significantly narrowed since the last time we tackled a similar query, a good few years back. Here's what springs to mind that's still around:
"In the all-new Las Vegas, it's sometimes fun to take a step back in time. And that's what you do when you walk into the Golden Steer, located about a quarter mile west of the Strip on Sahara. This place is old-school and it should be —- having opened in 1960, it's one of the oldest restaurants in Las Vegas. The bar and dining room are furnished in heavy dark wood, plush semi-circular high-backed booths, and memorabilia from the Rat Pack days. Frank, Dino, Sammy, Joey, and a host of heyday celebs ate here regularly, and plaques designating where they sat hang over selected booths (other famous guests include John Wayne, Tony "The Ant" Spilotro, Joe DiMaggio, Mario Andretti, and Elvis).
"Many on the wait staff have been here well over a decade (some over 30 years) and if you schmooze 'em a little, they just might 'take care of ya' (we were given two $12 martinis on the house, just because).
"The food? It's good. Steaks range from $32* for a petite filet to the $65 28-ounce porterhouse (most are $37-$42). Italian specialties are $24-$29, appetizers are $12-$16, sides are $5-$8, and cherries Jubilee or bananas Foster prepared tableside go for $12. You’ll like the meal, but the food definitely plays second fiddle to the joint."
*NOTE: The menu has changed a little since we last dined there, and the porterhouse is no longer on the menu, while steaks now start at $38 for the 8-oz petite filet.
"He was such a legend and -- if you knew him -- a real good man, but he was a hard man to get to know. He was a wonderful person who loved life and loved to eat."
Pignatello recalled how Sinatra's favorite meal was homemade cheese ravioli and calamari salad, always washed down with a bottle of Chateau Lafitte. Ole Blue Eyes was apparently also a dessert nut, his favorites being biscotti, St. Joseph pastry, and Boston cream pie -- all of which he would order, to round of his meal.
And that's about it. There are some other places with an old-school vibe, like the Bootlegger Bistro (past the south end of the Strip) and Casa di Amore (E. Flamingo), but the former post-dates the Rat Pack and we're not aware of them ever hanging out at the latter, although it's still a favorite of old-time Italian mobster types and has the vibe you're looking for.