James Blish 
Life For The Stars 
Cities in Flight Book 2

Science has come to humanity’s rescue with two crucial discoveries – antigravity devices that enable whole cities to be lifted from the Earth to become giant spaceships, and longevity drugs that allow their inhabitants to live for thousands of years – lead to the establishment of a unique Galactic empire.Now, the earth’s cities are able to abandon the worn-out homeworld for a new life, a new future. But what will they find as the hurtle off into the depths of space . . . ?