run down to
some place to travel to a place. (By running or any other means.) I have to run down to the store and get some bread. I want to run down to the bank, but my car is out of gas.
run down to someone or something
to come or go down to someone or something, rapidly. Sally ran down the slope to Bob, who stood waiting for her with outstretched arms. I ran down to the well to get some water for Ed, who had the hiccups.