Islamic school 480x631 Where is the best Islamic school in the world?Getty Images
Deciding what is the best is pretty subjective, so I will merely list some of the more prominent institutions:

Jami’ah al-Azhar (Egypt)
http://www.alazhar.org/

Dar al-Ulum Deoband (India)
http://www.darululoom-deoband.com/

Jami’ah al-Qarawiyyin (Morocco)

Ma’had al-Fath (Syria)
http://www.alfatihonline.com/

Dar al-Ulum Karachi (Pakistan)
http://www.darululoomkhi.edu.pk/

Dar al-Hadith (Syria)
http://www.daralhadith.com/historical/historical.htm

Dar al-Ulum Nadwah al-Ulama (India)
http://www.nadwatululama.org/