Question

Where is the center of islam located today

Answer 1

Islam is a religion, not a location. So there is no center. If you mean the holiest site, its Makkah. 

Answer 2

Mecca (مكة المكرمة‎) and Medina (المدينة المنورة‎)

Explanation ( Complete Oversimplification ):

The areas which are considered the centers of Islam are in Arabia in the cities of Mecca (مكة المكرمة‎) and Medina (المدينة المنورة‎). When the Ottoman Empire controlled these lands however, There was also the city of Konstantiniyyee / Constantinople (القسطنطينيه) which was the gateway from the Islamic world to the Christian world. Adding a little side note, Islam, like Christianity and Judaism, Is a RELIGION. It has had various locations over times from the Islands of Indonesia to Coasts of Morocco.