The phrase "keep one's eyes peeled" is used to mean staying alert and attentively looking out for something. It can also mean being watchful and vigilant. There are numerous synonyms for this phrase that one can use in place of it. Some of the most common ones include "stay on the lookout," "be on the watch," "keep an eye out," "remain vigilant," "be observant," "pay attention," and "be on guard." All these phrases convey the same meaning and are interchangeable depending on the context and situation. So, the next time you want to say "keep one's eyes peeled," consider using one of these synonyms to add variety to your language.