Jeb, I don't know of any stereotypes or stigmas associated with AA meetings. Such things are usually associated with people, not events. If you want to know about stereotypes or stigmas attached to alcoholics, there are probably millions of them. As has been suggested, go to a few different open meetings. No one's going to throw you out. But go with an open mind, not one with any preconceived notions of what to expect. If what you're doing is an observational essay, then objectivity is important. You need to write about what you observe, not about what you thought you'd observe.
If you think you may be an alcoholic, then listen to what's said in the meetings. You may hear your own story. As Carol suggested, go to several to see if AA is for you. But please remember that anonymity is of critical importance is AA. Leave the particulars regarding people etc out of your paper.