Boolocks sturm and rang.
Maybe old fuddy duddies yes frown upon it, but old fuddy duddies are the same in every country.
Holding hands, hugging, affectionate touching (not fondling) are fine in public. I see Japanese kids do it all the time in public.
In fact it seems Japanese girls LOVE hugs and being held, no matter where. Ditto with hand holding.
Kissing in public? Some girls don't like too, others do.
I think most cultures sucking face and french kissing in public is a bit frowned on really. But quicker lip kisses etc are fine for most girls. Just a time and a place. Wlaking in the park together? Fine. At a movie? Maybe fine. In front of all her friends? Questionable. In the shops? Maybe a peck.
Thing I've noticed here is that many things we are told about Japan aren't entirely accurate, especially when regarding youth.
Affection in public may have been frowned upon many years ago, but now, for most people, its not a problem.
And anyway, if you're fine with showing affection and your lucky girlfriend is fine with showing affection in public who really cares what some stranger thinks?