I don't want to visit my grandmother
Why don't you want to visit your grandmother?
I have better things to do with my time. Besides, it's my birthday, so I can do what I want.
It is normal to want to have an awesome birthday, but visiting the relatives that care about you is good too. Your grandmother might get the wrong impression if you don't go to see her.
I just don't care about doing things I don't want to do on my birthday.
You should always visit your relatives regardless, you don't know how much time they have left on this earth.