Where did Metallica primarily record the album known as The Black Album?

Metallica primarily recorded The Black Album at One on One Recording Studios in Los Angeles.

The sessions began in October 1990 and continued through June 1991, making the project a lengthy and demanding production. The band also worked for about a week at Little Mountain Sound Studios in Vancouver, while additional overdubs and mixing took place at A&M Studios in Hollywood.

Producer Bob Rock encouraged Metallica to record more collaboratively than on its earlier albums. James Hetfield and Lars Ulrich had often constructed rhythm parts separately in the past, but the Black Album sessions aimed for a stronger live-band feel. Rock also pushed for harmonic vocals and repeated takes until the performances met the band's high standards.

One on One is therefore the principal studio associated with the album, but it was not the only location involved. Mentioning only Vancouver or A&M Studios can be misleading because those facilities handled parts of the process rather than serving as the primary recording site.