The word "un-neatest" refers to something that is not neat or orderly. Antonyms for this word would include terms such as tidy, organized, neat, clean, and well-maintained. More specifically, synonyms for "un-neatest" would depend on the context it is used, and what qualities of neatness or orderliness are concerned. For example, "cluttered," "messy," "disorganized," and "chaotic" might be appropriate antonyms if referring to the state of a room or desk while "sloppy," "dirty," "unkempt," and "unhygienic" might be used when describing someone's appearance or lifestyle.