The song (sung in character by Donald Fagen) concerns a young runaway female who has fled an abusive father in Florida and who is now involved with the narrator, an older, affluent New York City man who views her as a temporary fantasy and muse. It begins with the narrator extolling the virtues of his new fashionably-attractive, young mistress ("the wonderwaif of Gramercy Park").
The chorus has the man jocularly mocking his young inamorata's naïveté and enchantment with New York City with phrases such as "Who makes the morning fabulous / Who says today's a fun day" and "Who makes the traffic interesting" with words and cadence of these lines spoken in juvenile syllables common to young American females.
In the middle verse - which name-checks upmarket grocery store Dean & Deluca - the couple gets some cheap alcohol ("A hearty gulping wine") and the narrator indulges his fantasy evidently acting out a role-playing scenario in which the narrator imagines himself to be Frank Sinatra in 1959, with Janie as a showgirl that Sinatra seduces.
The final verses take on a darker tone - the narrator suggests that they go for a weekend away to his friend Binky's "sugar shack" in Pennsylvania though he also hints that "Janie" may in fact be underage ("Or would that be a federal case?"). The final verse reveals that the runaway intends to bring along another female for a menage a trois or escapade ("Who has a friend named Melanie, who's not afraid to try new things?") and implies that the rendezvous fantasy must end imminently though the narrator leads her on ("Who gets to spend her birthday in Spain? Possibly you - Janie Runaway.")