A. raised
本句中Though raised in San Franciscos是省略的让步状语从句。Raise (="bring" up) 抚养：grow种植; cultivate耕作; 培养 (友谊等) 。如cultivate后接某人, 则意为“培养与某人的感情”。如：John always tries to cultivate the people, who are useful to him professionally. (约翰一向喜欢与事业上对他有用的人来往。)
本题译文：尽管在旧金山长大, 但戴夫米切尔总是愿意把小镇生活中平凡的事情记载下来。