My guess is that amending your past-year federal tax returns to correct the business address would not do any good. The city has already decided that you have to pay city tax, interest, and penalties. Also, it takes at least 5 months for the IRS to process an amended return, and its not clear that the city would even be notified of the amendment.
You have to reply to the notice that you received from the city with an explanation of your error, and try to convince them that your business is not really in that city. It would probably help to include some documents or other evidence showing your actual business address.
If you want further help, please identify the state and the cities involved. You might get a response from someone who is familiar with the specific city taxes and can give you more detailed advice. You might also want to consider consulting a local tax professional for assistance.
