Both forms - 'important to' and 'important for' - are correct, although there is a difference in meaning. Important 'to' suggests some kind of emotional attachment, whereas important 'for' suggests some kind of necessity. For example, 'It is important for me to get good grades in my end of term exams' or 'It is important for old people to have regular health check-ups'. These are practical needs. As you are presumably talking about an emotional attachment here, the better word to use is 'to'. Values and family are very important to me.

.... very important *to* me. Pero, "Values ad Family" no tiene sentido. Quieres decir algo como, "Values *and* family", probablemente.

Values and family are very important to me, [because I believe that Family Values lead to happiness]. Values and family are very important for me [to be happy in work and life]. Los valores y la familia son muy importantes para mí, [Porque creo que los valores familiares conducen a la felicidad]. Los valores y la familia son muy importantes por mí [ser feliz en el trabajo y la vida]. Estos son confusas, como por y para. La palabra "for" se utiliza como la palabra "por" al describir algo que es por causa de, o en representación de alguien o algo.

I think you will hear both "to" and "for" used. "For me, there is nothing more important than family."