Japan is way behind the US when it comes to non-smoking in public spaces. At last, Japan is heading to this (asahi.com in Japanese).
The most annoying thing while in Japan is a smoke-filled cafe! So many cafes and restaurants still allow smoking with a loose separation between smoking and non-smoking areas or even no separation at all that I hesitate to enjoy a coffee break.
In Japan, you can buy tabacco packages at a vending machine (the regulation on buying at a vending machine is getting tightened, though).
I'm very happy that most US states ban smoking in public spaces (List of smoking bans in the United States on Wikipedia). It's much less frequent in the US than in Japan that I get annoyed with somkes.