Shoes in Japanese Restaurants and Businesses
This is a big question for foreigners traveling to Japan, but I can assure you that the Japanese do wear shoes inside the majority of public buildings. Some service based businesses (places where you would spend more time than your average store) and some very old establishments adhering to Japanese tradition may ask you to remove your shoes and will supply you slippers to use while inside. Both my real estate agent and our local eye doctor ask that patrons remove their shoes and have a rack of slippers.
It is always obvious when you are expected to remove your shoes. As soon as you walk in there will be a genkan area and a rack where you are expected to place your shoes. Simply look for this rack as soon as you walk into any business in Japan.
Some of the more traditional izakayas and restaurants will be "shoes off" establishments. These places will usually have lockers in which to place your shoes. If you see a bank of lockers near the door, odds are you are supposed to remove your shoes. Some of the lockers will have a metal plate sticking out of the handle and some will not. That metal plate is your shoe locker key. The lockers without the key are in use, the ones with the plate sticking out are free. Place your shoes inside, remove the key plate and take it with you to your table.