To answer your question: You use "important for me" when there is something important that will lead to something else, usually implying good/favorable consequences. For example, "It is important for me to study hard so I can get a job and earn money". Here in this sentence, "study" will lead to the good consequence of "get a job and earn money". You use "important to me" when there is something that has a personal value or importance to you. For example, "This necklace is important to me because it was given to me by my mother" or "My family is important to me because they are supportive". In this case, the necklace has personal value (since it was given by a family member) and the family has personal or emotional importance, since they are also people who are close to you. In summary, use "for" when something important leads to something else (consequences) and use "to" when it has personal or emotional value to you.