My husband had this same concern - we live in a bigger city by far, but he has a high profile job as superintendent of the largest county's school system. He didn't start out with AA, but gradually started coming to meetings with me, not in the immediate area of influence and visibility he has, and gradually came to believe that he could go to a meeting anywhere and it was fine. Fine, meaning, he didn't fear being seen or outed- and has ultimately found that the benefits of living in recovery are so many, and include far better professional accomplishments, behavior and reception that even voluntarily mentioning to his bosses he is in recovery was actually a plus.
Anonymity, IMO, varies as people take it more or less seriously. In its intended form, it means that what happens in an AA meeting stays there, to put it succinctly. And everyone who is there has a life outside so anyone else is as likely as I am to think about "what if" non-alcoholics in their work or personal lives "found out." I have found some of the best people I know in the rooms of AA. Atlanta is a big city with a small town feel in many parts of the metro area, and certainly in the area my husband works and the part of town I grew up in - so I also found plenty of people in the rooms whom I already knew and thought very highly of, but didn't know they were also alcoholics like me.
Bottom line? I believe AA is worth it in every way.
My life and sobriety matter infinitely more than what anyone else thinks. Those who are negative or unsupportive have to be dismissed and any opportunities, if they are such, that I might miss out on because I am an alcoholic just aren't ones really meant for me.
Best to you.