Greenflower City was a major city on Mobius. Little is known about it before its destruction, but it was located within the vast Greenflower fields. When Dr. Eggman discovered a strange black asteroid emitting powerful Chaos energy, he built an enormous fortress and cannon on it. Willing to demonstrate his power to the world, he targetted Greenflower City and fired the cannon. When Sonic the Hedgehog made it to the city, it was already a pile of ash. It is unknown whether anyone actually survived, but it's implied the citizens were vaporized as well. The city i no longer mentioned at this point, and the story focuses more on the strange areas that Sonic and co. explore.
In Smash and Hyper's roleplay series, the story is a bit different as it still stands with people living. However, it suffered many disasters in the past, from attacks from various villains to people getting kidnapped and mutated and even having an outbreak of a new plague. The main heroes of the series live in the city, and do their best to keep it at peace.
In Splice The Hedgehog, the city is attacked by Dr. Eggman once again, who nearly burns the city to the ground with his robot army. The same heroes of the roleplay series drive him away, but the city is left in shambles. Some houses are left in unbelieveable states.