How do Percy and Grover travel back to NYC?
Percy and Grover travel back to New York City by plane. As the deadline to return the Master Bolt to Zeus approaches, they do not have time for any other form of transportation.
Percy knows that flying is off-limits for him because Zeus, the god of Heaven, currently suspects him of being the "lightning thief"—the one who stole the bolt in the first place. Percy takes the risk, as he has no other choice, and hopes that having the bolt with him will serve as "insurance": if Zeus decides to "blast him out of the sky," he will destroy his own bolt. However, Percy is still anxious all throughout the flight, and his fears are not unfounded. When he finally returns the bolt, Zeus grumbles about Percy's audacity. Poseidon, the god of the ocean and Percy's father, intervenes and calms Zeus down, thus reassuring Percy that he has made the right choice.
Percy and Grover travel back to New York City by plane.
This may seem a bit anticlimactic, but it's actually significant. Percy is a half-blood son of one of the "big three" gods, entangling him in a deadly prophecy; he's also been set up to look like the titular "lightning thief" when Zeus's Master Bolt appears in his backpack. As such, he's been warned not to fly anywhere, since the sky is Zeus's domain and to enter it might be construed as an insult.
However, Percy is returning very late in the book, after most of the novel's conflicts have been resolved. Percy takes it on faith that Zeus will forgive the trespass given the exigent circumstances. And he is correct; the flight occurs without incident.