The is Outside, by Andre Norton, published in 1975. It takes place in a post-apocalyptic domed city, that was built to protect the inhabitants from the polluted outside world. However, almost a decade before the events of the novelette, a plague had wiped out all the adults ("Olds") living under the dome, and the remaining "Littles" (young children) and "Bigs" (teens) have been fending for themselves ever since.
It has appeared with variations of these two covers.
A description of the plot, from this site:
Child survivors of some ecological disaster who live inside a sealed off dome city where the life support machinery is running down.... Andre Norton takes this premise, surely as old as sci fi itself, and finds a new solution aptly suited to the child readers this is intended for. Kristie, no longer one of the really little kids, but still young enough to be attached to her pet fox, is one of the young ones lured away by a Pied Piper known as Rhyming Man. And, following his trail of nursery rhymes and his motto, "Believing's Seeing," she finds herself led to the world outside the dome, now livable again. She also discovers that she has acquired the power of telepathy, and sets out to communicate the secret of escape to her big brother Lew. Anyone who knows his way around the genre will find this thin stuff, but the Rhyming Man is clever enough to lure those on the cusp between fairytales and sci fi.
The Rhyming Man (who appears outwardly to be the first "Old" that anyone has seen in years) does indeed appear to be some kind of hologram, and he leads Kristie, and later Lew, through a dance one a floor of disco-like square panels that illuminate when they are stepped on in the correct order, while chanting obscure nursery rhymes. After completing the dance, he teleports them outside the dome, to where the natural world is well on its way to recovery.