What is another word for having a look-see?
Pronunciation: [hˌavɪŋ ɐ lˈʊksˈiː] (IPA) 
When it comes to expressing the act of looking around or inspecting something, there are various synonyms that you can use instead of "having a look-see". Some suitable alternatives could be "having a glance", "taking a peek", "scoping out", "checking out", "surveying", "exploring", "examining", "investigating", "perusing", or "scrutinizing". Depending on the context and the intensity of the observation, these phrases can add a more nuanced and descriptive flavor to your writing or speech. So, next time you want to describe someone's visual activity, consider using one of these synonyms instead of the overused "look-see".
