If you take a look at a map of Copenhagen you'll see a whole bunch of districts with "bro" and a few more streets with -brogade:
Vesterbro, Nørrebro, Østerbro, +the district, Amager and the streets to go with them Vesterbrogade, Nørrebrogade, Østerbrogade, +the district, Amagerbrpgade. With them you use the preposition "på". The same with "Vestegnen" - a number of suburban districts called so as a hole. With almost all others the preposition "i" is used.