If I received a citation for public nudity, would it be to my advantage to appear myself on this type of charge or have a public defender appear on my behalf?

Representation is always a good option... even it it involves using the public defender.  You have received a citation, which usually involves "fine only" or fines with minimal potential jail consequences.  However, even a citation can have a negative affect on your life.  You are being cited for public nudity.  Every time you apply for a new job or you want to volunteer at a school function for your kids if you have children, you could be required to disclose your criminal history.  Even if you fail to disclose, they have the right to run your history and learn that you have a "nudity" charge on your record. A nudity charge could be something simple like, urinating in an ally.... however, the public often equates "nudity" offenses with "sexual deviance" offenses.  You need help to assist you with this charge if for no other reason than to avoid the negative consequences on future employment opportunities.
You can show up and try to represent yourself.  However, keep in mind that everything you tell the judge, the court reporter, the prosecutor, or any other court officer could and most likely will be used against you later.  For some reason, people think they can walk into court and the statements won't be used because a police officer isn't doing the questioning.... when in actuality... every statement is a voluntary, admissible statement.  A public defender or other attorney can appear for you, assert your defensive theories, and protect you from making statements that could result in a waiver of your right to remain silent.