Most definitely. It is called conflict of interest.
Editors of both large and small papers are often confronted with this dilemma. Louis Day, in his textbook Ethics in Media Communications, defines a conflict of interest as a “clash between professional loyalties and outside interests.”
In this case, the clash would be between your responsibilities as a city council member vs. your professional loyalties as a journalists. A fundamental duty of a journalists is to be an observers of events instead of participants.
In your case you would have the ultimate responsibility of the coverage of your city council. As a city council member, you would be acting on issues that have impact your community.
I think it is almost impossible to completely separate the two duties — there will come a time when your action as a city councilman will influence how you cover a story. None of us are totally objective creatures.