Since the heyday of swank eateries like the Brown Derby and the Stork Club, restaurateurs have known that nothing draws crowds like a celebrity clientele. Increasingly, however, the stars have begun to ask why someone else should make money off this phenomenon. Celebrities as stellar as Kevin Costner and Robert De Niro or as lunar as Al Lewis, who played Grampa in “The Munsters” 25 years ago, have bypassed the middleman and opened bistros themselves. Not all of them are in it to make a profit, of course. Some just want a tax loss. Others like to own their hangouts because they don’t trust people not on their payrolls to fawn over them properly; a few, like Mickey Mantle or Sean Penn, may want a place they can’t be thrown out of no matter what they do. Fans get a place to satisfy that insatiable American appetite for glamour, to share even the ephemeral communion with greatness that comes from eating a Dirty Harry burger at Clint Eastwood’s Hog’s Breath Inn in Carmel, Calif. “The attraction is obvious,” says Fred Sampson of the New York Restaurant Association. “Even if you aren’t in show business, at least you can dine with people who are.”

Some places are subtle, cloaking themselves in a spurious aura of exclusivity. Only the cognoscenti are supposed to know that the Tribeca Grill in downtown Manhattan is owned by Robert De Niro, Sean Penn, Christopher Walken and Bill Murray,which is why no gossip writer is allowed to mention it more than once per column. At the other extreme is the $15 million Planet Hollywood, which when it opens this week in New York is sure to set new dining-industry standards in publicity, interior decoration and souvenir jacket sales. The backers are Arnold Schwarzenegger, Sylvester Stallone and Bruce Willis, in partnership with producer Keith Barish (“Sophie’s Choice”) and Hard Rock Cafe magnate Robert Earl. The decor is by Anton Furst, the Hollywood designer who did the sets for “Batman.” His exuberant use of design elements such as columns sculpted to resemble Marilyn Monroe’s legs might almost make you think you’re in, say, Orlando, instead of down the block from Carnegie Hall. Exhibits such as the original knife from “Psycho” or the sledgehammer from “Misery” will give a whole new meaning to the phrase “tourist trap.” (Children will be warned away from these sights, although they will be allowed to view Jayne Mansfield’s bathing suit.) “I find it thrilling to see a garment or memorabilia that was owned by a star,” says Stallone. “It’s almost like eating in a museum.”

Yes, and the food (three pastas, four fajitas, five pizzas…) promises to be every bit as interesting, too. A few celebrity restaurateurs, such as retired baseball star Rusty Staub, are interested in good food for its own sake. Others, like B. B. King, whose new soul-food-and-blues club opened last May on Memphis’s famous Beale Street, at least seek authenticity. If you must listen to Howlin’ Wolf over a meal, B. B. King’s Mississippi catfish gumbo (or his specialty, Lucille’s Chili, named after his guitar) probably will sit better than Planet Hollywood’s vegetarian Reuben sandwich. For his part, Schwarzenegger admits he “never had any interest in the restaurant business.” But, he adds ingenuously, “I’ve always had a tremendous interest in things that are going to make a lot of money.”

Of course, people won’t go to Planet Hollywood for the food, although it will have to meet at least minimum standards of edibility for the restaurant to survive. It’s surprising how often that rule is overlooked. Ringo Starr’s Atlanta interpretation of an English pub, which combined the culinary standards of his native Liverpool with the welcoming manner of a rock-concert security guard, closed in around half a year. Steven Seagal’s restaurant in downtown Chicago made it only from last July to September, but it may be that someone who kills with his hands is the wrong celebrity to be peddling hamburger.

People will go to Planet Hollywood for the chance to be greeted at the door by Stallone’s famous scowl. This is about as likely as running into Roy Rogers at a Roy Rogers, although Planet Hollywood’s Earl promises that someone “of note” will always be on hand. Celebrity practices vary widely, and there are no rules about what constitutes misleading the public. Mantle spends an estimated 10 days a month at his Manhattan restaurant, while the genial Lewis actually has been known to stand on the street in Greenwich Village personally luring passersby into his modest Italian eatery, Grampa’s Bella Gente. Burt & Jacks, a pricey steakhouse outside Ft. Lauderdale, Fla., does not advertise that the eponymous Burt is Reynolds, but customers often ask about him anyway. “We tell them he’s back in the kitchen,” says partner Jack Jackson.

And for many, that’s close enough. Bliss to have eaten the same potatoes that went to Oprah’s hips, or a Lt. Dunbar Buffalo Burger at Kevin Costner’s restaurant and casino in Deadwood, S.D., or a Kenny’s Famous Stuffin’ Muffin at Kenny Rogers Roasters in Coral Springs, Fla. There will always be patrons like Mara Rosenberg, who will remember forever that special meal at Burt & Jacks-the time she almost met Burt Reynolds. “We were here one day and he was in the kitchen cooking,” she recalls. “At least that’s what the wine steward said.”

His Tribeca Grill is as popular with critics as it is with downtown New Yorkers.

72 Market Street has become an L.A. staple-and the piano player’s not bad, either.

Huge steaks and giant lobsters keep Floridians happy. Special features: fireplaces and a dress code.

Has two successful New York restaurants called Sam’s, but a third venture in Florida flopped.

His Chicago eatery celebrated opening night with a life-size bust in ice. It, and business, quickly melted away.

Atlantans were peeved when the ex-Beatle only showed up once at his short-lived pub, the Brasserie.