The phrase "hath look-see" is an old-fashioned way of saying "have a look" or "take a peek." If you're looking for synonyms for this phrase, there are many options available. Some alternatives include "check out," "inspect," "survey," "examine," "scrutinize," "peruse," or "browse." Depending on the context of the phrase, you could also consider using words like "investigate," "explore," "search," or "scout." These synonyms can help you add variety and interest to your writing or conversation, and give you more options when you need to convey the idea of taking a closer look.