A peak is the top of something; the highest point of a wizard's power, or the tippy-top of a mountain.
A peek is a quick look at something; a child peeking out from between her fingers, or a sneak peek of a book tucked in the back of another book.
Remember them this way: peAk has an "a" in it. "A" is for altitude, which is height. pEEk and EyE both have two of the letter "e" in them.