If you want a lawyer and cannot afford one, one may be appointed in a criminal case. If you want to fight this ticket, you should plead "not guilty" and get "discovery" from the prosecution. It may be that you can negotate a deal with the DA that would be acceptable to you. You may want to consult with a local lawyer for more specific guidance. Good luck.
Because this is a municipal charge, you have no right to a public defender. The guaranteed right to an attorney applies in criminal cases only. You may want to consider entering a not guilty plea and then trying to negotiate this matter with the City Attorney. While I do not necessarily suggest doing this without an attorney, if you are unable to afford an attorney, it would be best to still attempt to strike a deal with the municipal prosecutor before you go before the judge. In many instances, you can achieve a negotiated resolution. Be aware prosecutors tend to always want their "pound of flesh" so you will probably not walk away from this with an outright dismissal.