Thanks, Soo Mab. Your explanation makes sense! I can see your point!

"For" and "to" are both contextually correct. For example, as you have mentioned above "English is really important to me because I will have to live in NY in the near future" sounds fine.(Englishは私にimportantです) However, consider this: "Time management is very important for meeting deadlines"... in this case "for" sounds better. (Time Managementはmeeting deadlinesのためにimportantです)

English is really important to me because I will have to live in NY in the near future. In this case, it's better to use "to", right?

Oh　Thank you for your help. This is my first question ever. I'll keep studying English. Thank you so much.

It depends. I would usually prefer using "to me". If you are learning English to accomplish something else-- perhaps to find a good job or to move to another country then you should use "for me". I would finish the sentence with "English is really important for me to learn". ex. It is really important for me to do well at work this month. If you just really love English and think that it is an important part of your life you can use "to me". You do not need to have an explanation for this. ex. "My mother is very important to me." "Staying healthy is very important to me." "Money is very important to me."