From Sonic Retro
Babylon Garden is an ancient floating city (and a racetrack of the same name) which features prominently in the Riders series games Sonic Riders and Sonic Riders: Zero Gravity. The city was once the home of the Babylon Rogues' progenitors, a mysterious and advanced people known as the Babylonians. According to legend, the Babylonians incurred the wrath of the Gods because of their crimes, and Babylon Garden was "cast into the depths of the earth".
When rediscovered in Sonic Riders, the Garden is a lavishly decorated city of mosaic plazas and Byzantine domes. In Zero Gravity, the city is almost totally destroyed by the Arks of the Cosmos and the "Lightless Black", stripping Babylon Garden down to its original incarnation: Astral Babylon.
In Sonic Riders
Jet the Hawk, Wave the Swallow, and Storm the Albatross identify themselves as the Babylon Rogues throughout Sonic Riders, claiming descent from the ancient people of the Babylon Garden. Jet inherited a mysterious, cubic heirloom from his father on taking over leadership of the Rogues, which he (correctly) believes to be the key to finding the lost city.
Dr. Robotnik, interested in the treasure of Babylon for his own nefarious reasons, pays a surprise visit to the Rogues' airship. The fat man tells Jet that in order to find the Garden, he should gather the seven Chaos Emeralds (and put a stop to Sonic the Hedgehog while he's as it). This sets the Rogues on course for Metal City, to steal the gem and lead to the Night Chase level. Meanwhile, to facilitate the acquisition of the rest of the Emeralds, Eggman sets up the EX World Grand Prix, intending to have Team Sonic unwittingly do his work for him and bring the gems together at the final race.
The Doctor's plan is successful, as after the Grand Prix's final, the Chaos Emeralds do indeed activate Jet's cubic artefact. Babylon Garden rises up out of desert to hover over Sand Ruins. Eggman steals Jet's device and flies off to the Garden to steal its treasure, with Team Sonic and the Rogues in hot pursuit.
Sharing a name with its setting, Babylon Garden is the sixth Hero-story racecourse in Sonic Riders, and, predictably, takes place on the ancient floating city. Sonic and Jet land on the Garden and race off to stop Eggman from stealing the (as-yet unidentified) treasure. Pursued themselves by a host of E-10000G robots, the racers have to avoid Babylon Garden's still-very-functional defences in the form of silver-and-cyan fighter drones, which strafe the tracks with explosives - requiring Sonic to ride along their turbulence rather than on solid ground!
In addition to the "Babylon Garden" racecourse, Sky Road, Babylon Guardian, and (presumably) Digital Dimension are also located on the floating city. In Sky Road, Wave, Storm, Tails, and Knuckles flee E-10000R across the Garden's airborne plazas, arriving just after Sonic disposes of Eggman. While Team Sonic deal with an incensed Amy, the Rogues enter the temple to find at its center an impossible black void of apparently infinite dimensions. They are confronted by the final defence of the ancient Babylonians; Angelus the Gatekeeper, who manifests within the darkness. Sonic, Knuckles, Tails, and Amy speed in to help out as the door slams shut, to start the Babylon Guardian track. Angelus manipulates the holodeck-like interior of the Garden into a twisted hellscape (or a cherubic heaven, in Digital Dimension), and the final boss of Sonic Riders is on.
When Sonic defeats Angelus, the illusory genie disappears in a puff of smoke, leaving behind a rather clichéd treasure chest. Just as Sonic and Jet open it, Eggman reappears, dual-wield blasters in hand, and demands that they hand over the prize. The hedgehog obliges, and hurls a rolled-up carpet at him; at which Eggman curses that he organised an entire racing tournament just for a scrap of cloth, and gives up. Tails, however, notices that the carpet is made from the same materials used to make modern-day Extreme Gear... and sure enough, unfurled, the item floats just like a magic carpet.
In Sonic Riders: Zero Gravity
Sonic Riders: Zero Gravity revolves around the discovery of the Arks of the Cosmos: five bracelet-like meteorites which Wave contends were once part of Babylon Garden's engines. As the story progresses, Knuckles' translations and the Rogue's discussions suggest that the Garden may have an extraterrestrial origin. Finally, in the Last Story, the renegade SCR-HD robot gathers the Arks together at the top of MeteorTech's Crimson Tower, calling Babylon Garden into the vicinity and sparking an overload reaction which detonates the floating city's levitation engines. The truth behind the characters' conjectures is revealed as the unleashed black hole strips away the city's lavish mosaics and decorations, leaving behind only the ancient substructure: Astral Babylon.
It transpires that the Garden was indeed once a giant spacecraft, which malfunctioned above Sonic's world and was forced to crash-land, stranding the high-tech Babylonians. Sonic fights Master Core: ABIS on Mobius Strip inside the gravatic maelstrom buffeting the uncovered spacecraft. After the robot is defeated, the black hole subsides, leaving Astral Babylon floating in orbit.
In Sonic Rush Adventure
A suspiciously similar legend - about an advanced people who were cast down from the sky - surfaces in Blaze's world during Sonic Rush Adventure. The stage Sky Babylon is set on what may well be the transdimensional analogue of Babylon Garden.