While visiting Tokyo, I noticed that most levels were indicated by B2F, B1F, 1F, 2F, ... .
This doesn't look like the Romaji for -kai or -gai counter-words, which I assume would be chika ni-kai, chika ikkai, ikkai, ni-kai, ... .
Is it wasei-eigo for Basement 2nd Floor, Basement 1st Floor, 1st Floor, 2nd Floor?
This may be an answer to Derek's comment rather than to Andrew's original question.
They are commonly written on walls right in front of an elevator, stairs, or an escalator, or on elevator buttons. They stand for Basement 2nd Floor, Basement 1st Floor, 1st Floor, 2nd Floor, as Andrew wrote. In Japanese, when words are abbreviated, they are usually abbreviated in romanization or abbreviated after its English word. Writing F would require much less strokes than 階.
I did not know that they are wasei-eigo. Are they not used in English? Or, do you mean that the word order Basement 2nd Floor is wrong as English and should rather be 2nd Basement Floor or 2nd Floor Underground or something? If you mean that, then it might be wasei-eigo. The idea is something like 'negative 2nd floor'.
You already know what these signs mean, but let me try to answer your specific question: Are these wasei-eigo? A short answer is “probably no.”
Recall that a wasei-eigo is a word which looks like a loanword from English but in fact is made in Japan. Although the signs B2F, B1F, 1F, 2F, and so on are specific to Japan (and possibly some other non-English-speaking countries), I do not think that it is common to call them wasei-eigo. They are just “signs used primarily in Japan,” and it is not clear if they are words at all.
Sometimes people may abbreviate 地下1階 to B1F in writing, but even in that case, I guess that most people read it as ちかいっかい. This suggests that B1F is merely a way to write 地下1階 instead of a separate word in its own right.
Let me add my own opinion to the contrary.
The ...B2, B1, 1, 2... numbering system for floors was likely borrowed from some foreign country when elevator technology was first imported into Japan, therefore likely from USA.
As for the F suffix, it's probably from the English "floor", as the same word in other languages doesn't begin with F (To wit: Andar, Verdieping, Etage, Piano, Piso... just to list the languages most often used in Japanese loanwords.)
One might guess they added the F suffix because numbers in Japanese must always have a counter after them. You never say 2, you say 2人 for two people, 2匹 for two animals, and so on.
As for the choice of F vs 階, either printing technology on elevator buttons was not up to the task at the time (most likely) or B2階 looked wrong to Japanese eyes, or not "modern" enough to appear on something as futuristic as an elevator.
So yes, considering that B very likely stands for basement and F for floor, but nobody says B2F outside of Japan, I would consider them "English made in Japan" or wasei-eigo. And yes, a single letter or romaji acronym can count as a word in Japanese, see Hする and others.
