What is it like when you go to a alcoholics anonymous meeting?

You won't really get anything out of one meeting, much of what goes on in AA goes on outside of the meetings and members tend to turn it down when there are visitors. You especially won't understand why some are so opposed to it.

The idea behind you going is to show you a sanitized version of AA that you would feel good about suggesting it to people.

I'd suggest you read the 12 steps:

http://www.serenityfound.org/steps.html

(Folks in AA claim they are "spiritual, not religious" despite half of the steps focusing on God.)

then read this:

http://www.orange-papers.org/orange-rroot030.html

AA is faith healing, not treatment.

AA has about a 5% success rate, the same as no treatment at all, except is has a much higher mortality rate and rarely works with those who also have a occurring mental illness (about half of those in the rooms). There is a small, but vocal anti-medication, anti-therapy faction in AA that claims that if a person uses medication they aren't really sober and if they work the program properly, therapy is unnecessary and confusing, God will "restore us to sanity".

I wouldn't be surprised if many AA meets are religious. Replacing one crutch with another seems like a useful thing to do, even if the crutch it is replaced with is based on a work of fiction.