"That is extremely important to me."
Translation:Das ist mir extrem wichtig.
The pronouns tend to be as close as possible to each other, or better the whole subject-object thing. Now, German is very strict about the verb being in the 2nd position, so the dative pronoun is forced one position to the right to make room for the verb. Das ist mir ganz wichtig. - is really the only sentence that would make sense. Note that das (that) and mir (to me) are as close as possible to each other.
In certain cases I have heard people say ''zu mir''. Definitely ''Kommt zu mir'' for example. And I see nothing wrong in saying ''Das ist sehr wichtig für mich''. Es kostet dich keinen Cent or Es kostet keinen Cent für dich, or Es kostet dir keinen Cent, for me are also correct but mean different things, a native German speaker told me. You can check those in Google. However I would be grateful if anyone told me I am wrong and explain.