Can I use romex in my unfinished, detached garage or should I use MC?
New Jersey apparently is using NEC 2011 with some minor amendments that would not appear to affect the question.

I believe that means the wire needs to be "protected" and as stated in my comment I'd personally recommend EMT (lightweight steel conduit) first and foremost, though MC/AC also suits my concept of keeping it rodent-proof (and barring insane rodent pressure, PVC conduit also works.)