The phrase "having a looksee" has a playful and colloquial tone. Some synonyms for this phrase include "taking a peek," "checking things out," "doing a once-over," "inspecting," "surveying," "scoping out," "perusing," and "examine briefly." These phrases convey a sense of curiosity and informality. They are often used when someone wants to casually investigate or explore something without a specific goal or purpose in mind. Whether you're exploring a new neighborhood or looking over a document, these synonyms for "having a looksee" offer a fun and lighthearted way to describe the act of observation.