Young people don't know or remember this, but New York City wasn't always a safe, clean city filled with yuppies!
Back in the mid-Seventies, New York City was in a state of major decline. The city was dirty and polluted, the crime rate was very high (thousands of murders every year), middle-class and upper-class whites were leaving the city in droves... it looked to many as if the city was dying.
Worse yet, the city government was teetering on the verge of bankruptcy. When then-mayor Abe Beame asked the federal government for a bailout, then-President Gerald Ford refused (this was captured in the famous New York Daily News headline "FORD TO CITY: DROP DEAD"). And across the country, millions of people actually appplauded Ford for refusing to come to New York City's aid.
Since it SEEMED as if the city itself was dying, and it SEEMED as if the rest of the country hated New York and was willing to let it die, Billy Joel was inspired to write this fantasy song in which the government decides to annihilate New York. And 40-something years later, a bunch of former New Yorkers, now living in Florida, are reminiscing about their old hometown.