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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/