"Look high and low" is a common phrase that means to search everywhere for something. However, there are several antonyms for this phrase that describe the opposite action. If you want to avoid searching for something, you could "give up," "abandon," or "ignore" it. Alternatively, you could choose to "narrow down" your search or "limit" your options, instead of looking high and low. If you already know where something is, you could "retrieve" it or "locate" it easily without searching. Ultimately, there are many ways to approach finding something, and sometimes the best solution is to not search for it at all.