La Guardia, JFK, and Newark would all be linked by the high-speed shuttle circuit (which, since it’d be built from scratch, could be easily equipped with wireless, cable TV, and other forms of information-age distractions). Passengers and their luggage would be screened before entering each secure hub. Having security checkpoints throughout the system would help reduce X-ray-machine bottlenecks. Most important: no more $30-plus cab rides, ever.
Diagram by SHoP Architects  

While onboard the shuttle trains, passengers could check in luggage, shop duty-free online, and have a drink or two before disembarking at the gate.
Photo-illustration by SHoP Architects