One possibility for a transport network consists of large tubes (about 25m diameter) with 4 smaller 3m diameter tubes at their center (two in each direction - having two allows for maintenance with disrupting traffic flows completely). {A single tube could carry 80,000 people per day average, up to 300,000 a day at peak.)
The inner tubes would be in vacuum, and would allow pressurised carriages to be accelerated at a steady one G (10m/s).
Carriages would be magnetically levitated and accelerated above steel rails.
The large outer tube is required to isolate the inner tubes from any earthquake
or other movement.
In such a network travel times are quite short:
200km would take 5 minutes,
1,000 km 11 minutes,
5,000km 25 minutes, and
20,000km 48 minutes.
With a series of feeder networks to major hubs, no inhabited part of the planet would be more than two hours travel from any other part.
The system would be silent and hidden. No ongoing environmental effects (other than a little heat).
Surface carriageways could be low velocity and low environmental footprint, as even in remote rural areas they would only need to link up to about 5km maximum to a tube node.
Aircraft would be required only for isolated islands, or for sport.
With the energy and manufacturing facilities available, such a network could be up
and running within two years of completion of the replication phase.
Using one machine to bore out every 100m of tunnel would mean the tunnel borers
would only need to dig at 30cm per day to complete the tunnels in a year.
Underwater sections of the tunnel could be fabricated in space, and landed
on site for assembly (each one with it's own propulsion and bouyancy systems
to allow it to hold station under water).
In cities local nodes need be no further than 100m apart, underground links could conceivably join every dwelling.
Imagine living in rural New Zealand and taking less time to travel to New York for a show performance, than most people take to commute to work today.
People who traveled internationally regularly could have their carriages fitted with remote sensors that would allow customs to give them a clearance as they traveled, so that they experienced no delays on arrival.