@ Wolfman. Sorry, that won't work. A suburb is clearly a "Vorort". ("Haan is a suburb of Düsseldorf.") http://dictionary.reference.com/browse/suburb
My feeling (from the US viewpoint) is that "borough" is quite good, especially if it has some kind of governing structure (like the five New York City boroughs and comparable to the Bezirksvertretungen in larger towns in North Rhine-Westphalia). This is, however, probably not acceptable in UK English.
"Quarter" is another good alternate. Sometimes you have to flesh it out a bit: "the Eppendorf quarter within the City of Hamburg", alternately "the Eppendorf district within the ..."