"Importance of ＿ to" or "Importance of ＿ for"?

You could use either, but it's more common to use to in that context.

I think these two may have slightly different interpretation. The first one is about how one thinks of the importance of money in general (or in some particular context not necessarily related to that someone personally), the second one is about how money is important to someone.

This link may help to answer your question http://www.talkenglish.com/Grammar/prepositions-of-to-for.aspx. To is used to indicate relationship. The object has a relationship to the subject in its importance, so to is most appropriate. That is, "The importance of an object to a subject". So, in the example: "the importance of money to someone". Note, however, that "the importance of money for someone" may be commonly used, but the former is grammatically correct.