Although a city centre is where most of the grand and famous landmarks are normally found, it is far from the only area where good images can be created. Do some research, find a couple of suburbs that sound interesting, and then spend a day or two investigating what they have to offer. Don't be in too much of a hurry. Be prepared to visit specific areas at different times of the day in search of the images you are seeking. Light changes everything, and the streets themselves change early and late in the day when they are quieter.
Tired, old buildings can be far more photogenic than modern streets, so explore with an open mind. Look for areas undergoing renovation, demolition or reconstruction, and streets where problems are apparent. Some streets become isolated as the result of a new bridge or elevated highway being opened, and others may be decorated with graffiti. Such areas may say more about a city than its shiny new structures.