I have handled many of these summons for avvo users. Its a misdemeanor under the City Charter and you don't want to just plead guilty. The outcome will depend on what court you have to report to. If you were in Manhattan, its either 346 Broadway or Midtown Community Court on West 54th Street. I am always able to negotiate something favorable (more so at Midtown Community Court) and the client does not have to appear in court. I am a former federal and State prosecutor and now handle criminal defense. Please feel free to check out my web site and contact me if you wish to retain counsel.
Urinating in Public as charged under NYC Health Code Section 153.09 is a misdemeanor offense. Typically, the court at 346 Broadway will allow you to plead the case down to a violation under the Administrative Code (16-118) with a small fine, but my experience after years of practicing in that court, is that this is done in person, either with a retained or assigned attorney. Perhaps if the officer had charged you with only the Admin Code violation a plea by mail would be more appropriate, but I would not recommend it in this case where you're charged with a misdemeanor.
You may want to consult with an attorney, often the court will allow you to appear by attorney in lieu of your personal appearance.
Please feel free to contact me if you have any further questions.