Meeting the parents?

Ok, so me and my Japanese boyfriend have been dating for 2 years now, and he wants to take me to Japan this year to meet his family. I am very nervous, many of his family are very traditional and I don't know what they will think of me. I am very shy and quiet person.
When I meet his family, does anyone have any advice? Like what is not good to do or what would be polite or rude?

I am very shy and quiet person.

This will help you a lot. I am sure you will be fine . Japanese people or families are very kind and caring . So do not worry and enjoy your trip, Meet the parents , well... not American version.... lol.
Japanese families love giving gifts money etc... in my experience as I first met with my in laws and family friends.
They will observe you very deeply but will never show or say anything. You just be natural as you are .
It will be a wonderful experience for you when you find yourself among very beautiful , caring and loving people. You are also one of the lucky one on this planet who is going to be the part of beautiful Japanese family and society. Have a good trip .