In The Sopranos episode S03E03, "Fortunate Son" there is a scene where Christopher Moltisanti is initiated into the family. What is that place? As far as I know, it's the only time along the series we see that basement.
The best conclusion I can reach is that this is simply the basement of some unknown mafia member.
The episode doesn't specify what this place is, I can't locate a script and (having watched the show multiple times) I don't recognize the place either. According to the original Wikipedia episode recap (before it was truncated for space), this is just "the basement of a made man". It was probably applying logic, since this is where the Omerta ceremony often takes place (see this interesting article about the ceremony, which was based on existing testimonies and specifies that it's "usually done in a room or in the basement of a fellow mobster’s house"). And it makes sense to do it somewhere less prominent and more clandestine.
But besides replicating the real life ceremony, I believe this particular unknown location was also chosen by the show to convey:
- Secrecy - Just like Chris, even we don't know where we are and feel similarly disoriented;
- Mystery - It's a dark, spooky and ominous place;
- Shabbiness - But in contrast to the gravity of the ceremony, in reality this is just some crappy basement - which fits the show's theme of the traditional mafia's decline in modern times.