I thought I'd be able to clear this up for you, but the records are contradictory. My hunch is, it was recorded in LA. the Complete Motown Singles box set notes two of the songs (which were also issued on a promo 45) being recorded "at the Graystone Ballroom" but the write-up conflicts with this, referring readers to a photo in the booklet of the recording session. Marvin is seen in a recording studio, with a string section.
The website Don't Forget The Motor City, which I think is highly authoritative, notes "recorded California" for all the songs I've checked (one mentions additional work at a New York studio). My guess? The Graystone Ballroom credit was a ruse to make it appear as if he was live on stage, when really he recorded it in the studio.
I've been having a hard time finding out where this album was recorded. The album sleeve says The Graystone Ballroom in Detroit, but producers Hal Davis and Marc Gordon were based in Los Angeles, so it's likely the album was recorded there, possibly at Sound Recorders.