Translation:Family is more important to me than other things.
"Important to me" is used for something you value highly, "important for me" for something that you need for something, for your work or your life.
I must ask the same question as jakub as the explanation provided by vladafu does not hold water in these circumstances for me as a native english speaker. In the circumstances referred to by vladufu i would accept his explanation but not in this case where there is a difference in word order. It would be more natural in this sentence for me to use 'for me' rather than 'to me'. In fact i think, with respect, vladafu has missed the point.
I am not a native English speaker. I depend on textbooks, dictionaries, corpora and similar resources.
In this case I found this and I based my answer on that:
When you mean that you care about something a lot, say that it is important to you, not that it is ‘important for’ you.
I can easily be wrong.
Thanks for responding. I read the reference and as i said there would appear to me to be a difference in usage. When you say family is more important to me that is correct but if you say 'for me family is more important' this would be common usage stating the importance of family. I would suggest it is the word order is the issue here. Starting with for me emphasises this statement. Brian
"family is more important than other things to me" should also be correct... Word order doesn't matter
Perhaps even... To me, family is more important than other things