Japanese women don't express affection in public
Understanding Japanese women
Japanese couples don't usually demonstrate affection towards each other in public places.
Public displays of affection between members of the opposite sex—such as kissing and hugging —are considered rude and should be kept private. Public display of affection might not be common, but it is certainly not forbidden either. Holding hands perfectly accepted.
Useless to say but, no kissing in front of friends, co-workers, or family membres.
Moreover family members almost never touch, hug or even display physical affection in public places. The majority of school children have declared they have practically never witnessed their mother and father kiss.
Holding hands and even hugging among members of the same sex is completely accepted despite the fact that this practice is less than common in Japan than other countries in Asia.
In Japan, if you want to be polite and respectful and not make some people feel uncomfortable (girlfriend, wife), don't impose YOUR ways. Try to refrain from displays of affection in places where people are around.
Your Japanese girlfriend isn’t stopping you from kissing her on a street corner in Shibuya because she doesn’t love you; she’s stopping you solely because public display of affection is taboo in her culture and she is uncomfortable with it. Understand the difference.
So, don’t be worried if your girlfriend doesn’t express her affection in public, modesty, respect for other (not embarrassing them by seeing you kissing and hugging) and blending are part of Japanese society.
You may disagree regarding fundamental cultural issues simply because you were each brought up with differences that manifest in unexpected ways, but as they say, "In Rome, do like the Romans do."