The Justice League has almost always been based in space. In the late eighties they built a geostationary satellite which was used until 1998; and after its destruction they moved to a tower located on Earth's moon. A second satellite was built in 2004 but abandoned shortly afterwards when the JLA was disbanded, though it remained locked in geostationary orbit.
Following the impersonation by a White Martian of a returned Superman and the framing of Justice League members as criminals, the Justice League satellite was destroyed by missile strike on the order of President Luthor. The first order of business for the newly formed JLI, then, was the building of a new base. The new satellite was built with the help of the technical expertise of Foundry and Steel Shiva; the brute lifting strength of Superman Secundus and Green Lantern; and the generous donations of companies like Wayne-Powers and Adani Energies.
With the help of their super-powers and money from major backers, including corporate and governmental funding from around the world, a new satellite has been assembled. In geostationary orbit over Metropolis, the satellite features some of the cutting edge technology pioneered by STAR Labs, Professor Quantum and the companies from the “Avenue of Tomorrow”: anti-gravity plating, teleportation to any point on Earth visible from orbit, teleportation back to the satellite from special booths scattered around the Earth, a specially built med-bay to deal with non-human medical emergencies and even an on-board salt-water pool for Atlantean visitors.
The satellite includes some basic weaponry which the JLI insist is principally for space-based defence – but the presence of extra-national orbital weaponry is a sore point for many governments, including the United States of America.
The current Justice League Satellite is overseen by the AI Parvati, created by Akshay Adani and uploaded from his private mansion to the Satellite. Parvati looks after all autonomous systems and assists in monitoring media and press for suspicious activity and is the central nervous system of the Justice League communications system.
As well as the teleport stations to enable transport to and from the Satellite, it has a complement of six shuttle craft for getting to and from Earth and the Moon. They are capable of travel within Earth's solar system, but not interstellar travel. Even travel further than the Moon would take weeks rather than hours. These shuttles are named for flightless birds: