If your ultimate goal is for your family and friends to not find out about this matter, pleading guilty is not a wise thing to do in the long run.  While a guilty plea will "put this behind you" in the short run, you must remember that guilty pleas/convictions remain part of your permanent record.  What this means, from a practical perspective, is that if anyone runs a background check on you (possibly for the rest of your life) the fact that you plead guilty to public indecency in 2009 will show up.  I recommend consulting with and/or retaining a criminal defense attorney to determine whether there is a valid defense and/or basis to have this charge dismissed, nolled, or otherwise found not guilty, so as to erase any permanent record of it.  While this may increase your likelihood, in the short run, of getting "found out" by family/friends, I believe this is the wisest decision to protect your interests in the long run.