The cast of “Cats.” (Matthew Murphy)

NEW YORK — “Cats” is wrapped up almost entirely for me in recollections of my daughter, seven years old at the time, accompanying me to the show and being so riveted that afterwards she memorized the photos and names of every one of those undulating felines.

“No, dad, that’s Mr. Mistoffellees!” she’d correct me impatiently, after I’d point to a picture in the souvenir materials and pull some cat character’s mangled name out of my head, something on the order of Mr. Jellydots or Munkusjerrie or Rum Tin Tin.

Seventeen or so years on, Lizzie not only barely recalls her “Cats” fixation, but when I asked her to come back with me to the musical — a slavishly faithful revival that had its official opening Sunday night at Broadway’s Neil Simon Theatre — she shrugged it off. Her “Cats” phase had long since elapsed.

How times change. Well, for us maybe. But not for “Cats.” The show at the Neil Simon, around the corner from the Winter Garden Theatre — where it opened in October 1982 and ran for an astronomical 18 years and 7,485 performances — is a virtual computer-scanned reproduction of the original; among the returning participants are director Trevor Nunn and set and costume designer John Napier. And so “Cats” remains precisely what it always was, a tuneful ball of coiled dancers’ energy and the useful vehicle for a discovery of the wonder of musical theater, most especially when a wide-eyed seven-year-old is in tow.

Owing, though, to a rather unctuous source — T.S. Eliot’s “Old Possum’s Book of Practical Cats” — the musical also is still a patchy vaudeville whose seams often show, particularly during the lesser numbers, like the patience-trying “The Awefull Battle of the Pekes and the Pollicles.” (If you’ve ever heard comedian Mario Cantone’s hilarious ranting about the self-conscious whimsy of “jellicle” cats, you can never again take the show’s poetic flights completely to heart.) Andrew Lloyd Webber’s pleasurable score — with its shameless repeating of a few majestically swelling themes — does still touch the warmest of familiar chords.

And whatever other misgivings you might have, wading through the thin story of the ascension of Grizabella the Glamour Cat (British vocalist Leona Lewis) to the redemptive Heaviside Layer, the cast assembled for the revival is gangbusters. Andy Blankenbuehler, the Tony-winning choreographer of “Hamilton,” has been recruited to tweak the dances of “Cats’s” original choreographer, Gillian Lynne (another Tony winner). His refinements inject precision and verve and allow several of the performers, in their equitably distributed spotlight moments, to show off grandly. Among the most exciting are Ricky Ubeda as the magician cat, Mistoffelees; Tyler Hanes, playing Rum Tum Tugger, the rock-and-roll cat, and Jess LeProtto and Shonica Gooden as the mischief makers Mungojerrie and Rumpelteazer.

Christopher Gurr portrays Gus the theater cat, and in tandem with Sara Jean Ford’s Jellyorum, who narrates Gus’s story — many of the songs are simply biographical sketches — the sweet ballad of Gus’s days on and off the stage is touchingly played out. Quentin Earl Darrington (Coalhouse Walker in the Kennedy Center’s revival of “Ragtime”) here gives a sturdy operatic heft to the patriarchal cat Old Deuteronomy, and Jeremy Davis brings an air of suavity to “Skimbleshanks the Railway Cat.” Lewis, for her part, is blessed with power to spare but is emotionally inert. No one will ever erase the memory, it seems, of Betty Buckley’s chills-raising rendition of “Memory,” in her standard-setting Broadway turn as Grizabella many moons ago.

Napier reliably has recreated the garbage-strewn lot where the cats gather for the annual Jellicle Ball, which is danced by the ensemble with dazzling spins and unison ferocity. The costumes, too, from the wild, streaked cat ‘dos to the furry leg warmers, take an audience back to the “Cats” of 1982. Which for families with little ones, in search of diversion from the tense events of the present day, may feel like time-travel worth the exertion.

Cats, music by Andrew Lloyd Webber, based on the poems of T.S. Eliot. Directed by Trevor Nunn. Choreography, Andy Blankenbuehler, based on Gillian Lynne’s original work; sets and costumes, John Napier; projections, Brad Peterson; sound, Mick Potter; lighting, Natasha Katz; orchestrations, Webber and David Cullen. With Eloise Kropp, Christine Cornish Smith, Andy Huntington Jones, Daniel Gaymon. About 2 hours 20 minutes. Tickets, $59-$149. At Neil Simon Theatre, 250 W. 52nd St., New York. Visit or call 877-250-2929.