I might be wrong but I would say that a +0 treshold would be a "just moved in" bachelor place. A Public place would be a -0 (or -1) as no one actually calls that place home. (A side thought, a well run, good public shelter could be a +0 or +1 treshold despite being public)
The idea of a negative threshold disturbs me. If I apply this to the rules and consider the role of a threshold "as a suppressor", a magical being would actually gain strength! Maybe you want just want to imply that there is so little threshold, a ward would find no foundation? (Which was actually one reason why I asked if +0 meant anything in the first place.)
Public buildings like English Pubs, Libraries (old, well-loved ones), Greasy Spoon cafes (with regulars) and old book shops may have a threshold of -0 depending on the circumstances. Anything where a few people have been there for a long time, anywhere with a lot of history and personality, might have a -0 threshold.
Is there a typo here? Because it seems to be an argument for a +1 threshold, which appeals to me. These are definitely special places and "normal" public places have +0 threshold anyway.
Oh, and why do you differentiate between -0 and +0? I know fate point costs consistently use -0, but using it anywhere else doesn't make (mathematical) sense to me.