Our club conducts a homebrewing demonstration and information tent at the annual Maryland Microbrewery Festival. The festival is on private grounds, and we are invited by the owner/festival sponsor.
The single biggest request we get from visitors to our tent, is "Can I have a taste of homebrew?" Because the festival has a beer event permit from the County, and microbreweries are there serving their beers to patrons who pay to get in, we are not allowed to serve samples of homebrew. It is frustrating, but we've gotten over it. We have asked, to no avail, to be allowed to serve small samples.
Other than that annoyance, the venue is a large draw for several thousand guests, so we have a built-in audience that is already interested in beer. The tent can get very busy with people walking through to get a look, and it requires several people dedicated to hovering over potentially careless guests (who have been drinking beer) to keep them safely away from hot kettles and burners.
We also used to publicize our annual Big Brew event which is held at members' homes. We used to draw a few occasional curious onlookers, but that was pretty much it. Because we also do the festival, we stopped trying to make Big Brew a public event.
So my suggestion is, try to hook up with a festival or other event/venue where there are already people interested in beer.