Final answer:
Grover and Percy travel from their school to New York City in a luxurious limousine that belonged to Percy's family, which was referred to as a 'station wagon' and is part of their secretive and exclusive journey.
Step-by-step explanation:
The question asks about the means of transportation utilized by Grover and Percy on their journey from their school to New York City.
When Percy invites his friend to "get in" their trunks were being loaded onto an ebony roof of the limousine, which suggests they used a luxurious and perhaps inconspicuous car for their initial travel.
This mode allowed them to avoid drawing attention from the people at the train station and the locals in Fish.
Additionally, there's mention that they drove on a road-tapestry brick, which emphasizes that they traveled on an exclusive path, owned by Percy's family.
Which led them to a very private place where the United States boundary ends, hinting that they were headed into an area that might not conform to the typical geographical and political boundaries as understood by the general populace.
The journey described is one shrouded in secrecy and exclusivity, leaving conventional forms of public transportation behind.
Instead, Percy and Grover experience a transition from humble beginnings to one of opulence and covert luxury — as evidenced by their transportation in an old car referred to as a "station wagon" that's potentially only considered 'junk' in the context of Percy's affluent lifestyle.