Early in a new production of Neil Simon’s “Plaza Suite,” Karen Nash, a middle-age matron who is one of three characters played by Sarah Jessica Parker, informs a bellhop at New York’s storied Plaza Hotel that his place of employment is rumored to be on the chopping block. “It’s an old luxury hotel,” she explains to the incredulous young man. “Today it has to be new. Old is no good anymore.”

Unfortunately, the lines could also apply to Simon’s play, now being revived on Broadway for the first time since its 1968 premiere. By the end of this roughly two-and-a-half-hour production, that gap doesn’t seem surprising. 

Although it was adapted into a fairly successful film in 1971 — a vehicle for Walter Matthau, Maureen Stapleton (a star of the original staging) and Lee Grant — the cold, hard truth is that this three-act comedy has not aged gracefully. 

Tracing two couples and a pair of old flames who visit the same hotel suite over the course of several months, the play trots out clichés about men, women, and marriage that were already growing stale when Simon channeled them. It’s all fueled by jokes and observations that run the gamut from charmingly quaint to flat-out hoary. 

So why roast this chestnut again, you may ask? The answer is obvious: to lure fans of Sarah Jessica Parker and Matthew Broderick — her real-life husband and co-star in each of these vignettes — out for a night of celebrity-gazing and escapist entertainment. Under the light touch provided by John Benjamin Hickey, a consistently winning performer making his Broadway debut as director here, the production does succeed, at points, on both counts.

The better moments of “Plaza Suite” unfold after the plodding first act, in which Karen and her husband, Sam, arrive at the hotel, its plush accommodations well represented in John Lee Beatty’s period-savvy set. The couple’s stay will coincide with their wedding anniversary, though Sam doesn’t remember this at first, and Karen may be confused about what day it is — factors that will figure into an ultimately unfunny portrait of a dizzy, needy woman and her selfish, condescending spouse whose insensitive comments to his wife made some audience members gasp at a recent preview.

Mr. Broderick has in recent years bucked his eternally boyish likeability by playing a few more menacing characters on stage and screen. But Sam isn’t creepy; he’s just a banal jerk — even if some of his gentler, more introspective lines suggest that Simon may not have seen him entirely that way. 

Karen, in contrast, suffers from no inner conflict; Sam is her life, and her one-track devotion — manifested even in her nagging and sulking — becomes sadder as the act progresses. Ms. Parker manages to add some comedic flavor to her frothier lines, though even in a frumpy dress suit the fastidiously slim actress doesn’t look out of shape, as her character professes to be.

The performers plainly have more fun in the second act, as do the characters they play: Jesse Kiplinger, a Hollywood producer who, thanks to costume designer Jane Greenwood dresses like Austin Powers; and his high-school sweetheart, Muriel Tate, who even while starting her own family has been keeping tabs — obsessively — on her successful ex-boyfriend.

If Jesse isn’t as patently miserable as Sam, he’s arguably even less evolved in dealing with the opposite sex, trash-talking his ex-wives and even his mother as he extols Muriel’s spiritual purity — unaware, as men like this tend to be, of the reasons behind his former girlfriend’s renewed interest in him, however nervous or reluctant. The actors manage an amusing chemistry as Muriel drinks herself into a looser mood, even if the premise of a guy trying to seduce a gal who’s had one too many is no longer considered as hilarious as it was during the Johnson administration.

The third act is by far the most entertaining, even if you won’t find its central characters more endearing than the others. Norma and Roy Hubley at first seem to have just one problem: Their daughter has locked herself in the bathroom on her wedding day. Where physical comedy figures into the previous acts, Mr. Hickey and his star performers up the ante here as both parents resort to increasingly desperate measures to pry the bride from her refuge, with some genuinely funny results.

Mind you, we also have to watch Norma and Roy bicker and whine about the pettiest and most predictable matters, among them the cost of the reception and everything associated with it. For an ostensibly light comedy, “Plaza Suite” delivers a vision of long-term relationships that is almost as depressing as it is dated; you’ll be relieved when it’s time to check out.