Mahoutsukai ni Taisetsu na Koto (2003)

Yume Kikuchi, a girl who can use magic, goes to Tokyo to be an apprentice mage to the handsome Masami Oyamada (a professional mage). In Tokyo, Yume learns about magic, helping people, and various other things on her way to being a mage. But she soon also finds out that even just magic alone isn't enough to make someone truly happy... (Source: ANN)