I had to make a quick stop at the....before going to work.
I had an errand to run before work と
I had to take care of something before work は
「仕事前に大事な用事があったから」。という意味です。
I had to make a quick stop at the post office before going to work. は (仕事前に郵便局にちょこっと立ち寄らないといけなかったの)。という意味です。
Making a Quick stop. は ちょこっと立ち寄ることです。