Best check with the ward office.

Hello from Mido :)
Yes... the recycling system is very very confusing here in Japan.

On every ward or city, there are garbage recycling rules, and the best way is to check your ward/city office website. Depending on the ward you live, there are even areas where you don't have to recycle much (this is because they have a high temperature incinerator)
However, there are two types of recycles where you can do at anytime, and that would be the plastic bottles and glass bottles. You can find the trash bins for them at any station or street next to the vending machines, and you don't have to worry about peeling off the logo or the cap. :)
FYI... if you are in a hotel in Tokyo, you don't have to worry about separating the trash at all.