What does Peter admire about Anne in The Diary of Anne Frank?

It's true that opposites attract, and hence the traits Peter admires in Anne are all the ones he does not share.
While Peter's shy, introverted nature makes it difficult and awkward for him to open up, he describes Anne as "never at a loss for words" and says that she "knows exactly what she wants to say and isn't the least bit shy." Peter comes across as a deep thinker who probably would have a lot to say if he had the confidence to speak up for himself. Though as a young teenager herself, Anne does at times feel turbulent, she is always confident in who she is as a person and does not hesitate to stand her ground when she feels strongly about a matter. This confidence is one of the main reasons Peter feels slightly awed by her.
Another admirable quality Anne possesses is her unique ability to project true joy. Despite the terrible circumstances this young, energetic girl finds herself in, she tries hard not only to keep a positive attitude herself but to remain outwardly cheerful for the sake of the others in the Annex. Peter says to her, "I think you’re just fine. . . . What I want to say . . . if it wasn’t for you around here, I don’t know. . . ." The happiness Anne fights to keep and radiate is what has endeared her to so many readers, and it endears her to Peter as well.
In short, Peter, as a sensitive and introverted teenager, admires Anne because she is so little like him. Anne's intelligence, playful curiosity, emotional strength, and assurance of who she is and what she wants from life are all reasons why Peter admires and may even be in love with her.