The phrase "run around" typically means to engage in pointless activity or to be constantly busy without achieving anything. There are a number of synonyms for this phrase, including the words "bustle," "hustle," "scuttle," and "dash." Other synonyms for "run around" include "flit," "flitter," "dart," and "skitter." All of these words convey a sense of busyness and activity, but without necessarily implying that anything of substance is being accomplished. Whether you're running around to get things done or simply trying to look busy, there are plenty of synonyms to choose from that can help you capture the spirit of this phrase.