The Arabic Islamic Institute in Tokyo is located near the Embassy of China and next to the Embassy of San Marino. It took me about an hour to find this place. I asked many people wandering around the area but they seemed scared and could not help.
I think the best strategy for finding the Arabic Islamic institute is to not look for the Embassy of San Marino, as while you can see the Arabic Islamic Institute behind the Embassy of San Marino, there is no access to it. So, I think what you should do is to find the Embassy of China, which is massive and has guards at about every 10 feet and then just keep walking around the Embassy of China until you find the Arabic Islamic Institute.
Upon finding the Arabic Islamic Institute, it had already closed since it took me so long, so I also suggest setting out early. Definitely bring a map as the people around might not be able to help you (even the guards around the Embassy of China).