Both are possible. As a simple statement, you can say either 'This is important for me' or 'This is important to me'. The sentence with 'to' sounds more personal and emotional/subjective, but the meaning is pretty well the same. But note that you can only use 'for' in a more complex sentence. For example: 'It is important for me to get a good mark in this test.'

In your examples, there is little or no difference. But in some cases, there is a clear difference: - It's important to me to be on time. <= to me personally, it is important that I be on time - It's important for me to be on time. <= at my job (for example), it is important that employees be on time

to me is correct