This was one of the meeting places of the Sons of Liberty. The attraction of this particular tavern may have been the library, which included many anti-British books. Or it might have been its reputation as the finest punch-house in Boston. Or it might even have been its location, which is right down the street from the Old State House, where the legislature met (and where the Boston Massacre occurred). Or it might have been Darts Night.
While I'd love to use the fact that the Patriots met in taverns to imply all kinds of things about them, I should point out that taverns were places to do business as well as drink, and that alcohol was viewed as (more or less) the cure for all ills. (You're waiting for a punch line, but that's actually true. Those are the kind of doctor's orders I crave.)