The following address plate is affixed to the outer wall of Ai Weiwei's studio in Beijing:
The same plaque may be seen outside the studio in the opening shot of this video. Thus, it would seem that Ai Weiwei's studio is located at 258 Fake St. in the celebrated Caochangdi arts district of northeast Beijing. So far as I know, however, there is no "Fake St." in Caochangdi. Furthermore, in his guise as architect (he collaborated on the Bird's Nest [Beijing National Stadium]), the address of his design studio is given as:
Caochangdi doesn't really have street names, which is why it's so hard to navigate. Some galleries make maps like the one here to help people get around (Fake is across from Boers-Li).
Let us assume that "FAKE" is a Pinyin (alphabetical) transcription of two Chinese characters.
Probably the most frequent pair of characters that can be matched with "FAKE" is fǎkē 法科, which would mean "section of the law" or serve as an abbreviation for fǎlǜ kēxué 法律科学 ("legal science"), neither of which would be appropriate in this instance.
Next would be fākē 发科, which could refer to humorous actions and expressions in traditional opera, passing the traditional civil service exam, etc. This, too, would not make sense in the present context.
There are a few other possibilities, but most have been used primarily in pre-modern times, are of much lower frequency, and are unsuitable for the sign outside of Ai Weiwei's studio.
Far more frequent today is fǎkè 法克 (lit., "law-subdue / overcome" or "Franco-Croatian"), as in the name of the fǎkè yóu 法克鱿 (scientific name Pedicabo Squid [from the first line of Catullus' "Carmen 16": "Pedicabo ego vos et irrumabo"]), i.e., "fuck you".
Consequently, the FAKE on Ai Weiwei's address plate (and in the name of his design studio) = "fuck", a word that he is quite fond of.
I'm not sure whether the managers of Caochangdi systematically assigned numbers to the various studios in the district. If they did so, then 258 is simply a number, but if Ai Weiwei picked that number himself, then it is sure to be pregnant with meaning. Contemporary, hip Chinese are given to punning on the names of numbers. With that in mind, a friend comments:
The only plausible homophone that comes immediately to mind for èrwǔbā 258 is ài wǒ ba 愛我吧 ("love me") which makes sense in context if you read "Fake" as if it were Pinyin. There are brands out there that use similar homophones — a brand of Taiwanese (?) women's cigarettes is called wǔ'èrlíng 520' ( wǒ ài nǐ 我愛你 ["I love you"]) and has little hearts in the filters — but I'm just guessing here.
Another friend suggested:
258 could have no meaning at all, but I'm going to over-interpret for a moment: Perhaps "258" (二五八) is a scrambled version of "250" (二百五), the latter meaning "not all there."
Last minute notes on 258 provided by Jason Q. Ng:
This recent Times article says 258 is the street address.
Further color images flutter past on a dozen monitors in “258 Fake,” an ebullient document of his life centered on a studio populated by friends, assistants and cats. (Mr. Ai calls his studio Fake, and 258 is its actual street number.)
Foursquare lists the exact address as 草场地258号, Beijing, Beijing (link plus map).
Looks like "草场地" is indeed enough of a marker for that street 258 Fake is apparently on. Though 258 Fake isn't listed on Google or Baidu Maps, the address for 256 is located at the spot which corroborates the Foursquare marker for 258 Fake.
I went through Baidu Maps and wrote in what the numbers were for that area into the attached/below image. [VHM: omitted here, but available upon request] I have no idea what the logic of the numbering system is. If Baidu's addresses are right, it seems pretty haphazard.
Oh, I almost forgot. In styling his studio "FAKE", Ai Weiwei is almost certainly also taking a sardonic dig at the epidemic of fakery that plagues Chinese society and culture.
[Thanks to June Teufel Dreyer, Joan Lebold Cohen, Anne Henochowicz, Kara Simon-Kennedy, Brendan O'Kane, and Kellen Parker]