Remove your shoes

I don't typically remove my shoes to eat dinner in a restaurant, but when it is the business' policy, I follow suit.  It isn't uncommon to have a restaurant in Japan require shoes to be removed while dining at their facility. 

I've never made the mistake of wearing shoes inside a restaurant where they should be removed.  There isn't a big sign saying "take off your shoes"!  Instead, you have to look at the environment and pay attention.

Most times, there is a step up, just like in a house, from where you enter to the "dining level". 

There are also typically lockers for you to store your shoes next to the entrance.  There is a key that simply slides out that you take to your table with you.

Finally, there are almost always shoe horns to help get your heels back into your shoes since there isn't a seat to help you.

I don't know why you need to remove shoes in some restaurants and not in others, but it is important to follow the rules.