There are many synonyms for the phrase "having a look." Some common alternatives include "taking a peek," "glancing," "inspecting," "examining," "scanning," and "surveying." Each of these phrases conveys a slightly different connotation, so it's important to choose the one that best fits the context of your sentence. For example, "taking a peek" suggests a quick, casual look, while "inspecting" implies a more thorough and detailed examination. Whatever synonym you choose, remember that the key to effective communication is choosing language that accurately conveys your intended meaning.