I'll let others weigh in on public space vs. my apartment. I just moved to Madison from Washington, DC where there are frequent Mustachian meetups in private homes. So I have been to enough Mustachian homes that I personally don't feel squeamish about it. But I understand that others might be more nervous about meeting strangers from the internet in a private home. If it helps, arebelspy (MMM forum moderator extraordinaire) and his wife attended a meetup at my home before I moved here- I'm sure he would vouch for me!
That said, if the group seems to prefer a public space, I would suggest Johnson Public House.