The phrase "came round" has various synonyms that could be used depending on the context. One of these is "stopped by," which may imply a brief visit or a drop-in. "Visited" works as well, indicating a planned or unplanned arrival, as does "arrived" but with less emphasis on the social aspect. "Called in" or "popped in" often suggests an informal or friendly visit, while "showed up" could imply a more formal or possibly unwelcome appearance. Other synonyms for "came around" may also include "came by," "swung by," "dropped in on," or "stopped in." As with any expression, context is essential in choosing the most suitable synonym.