In Africa, I've only been to UWEC (Uganda Wildlife Education Center) in Entebbe several years ago but was quite impressed. I think it could make the Top 5, and definitely is #1 in East Africa.
I've heard Mysore, Delhi and Nandankanan as the top 3 in South Asia. Of course, zoos in East and Southeast Asia will beat these. Singapore Zoo (or WRS in general) should be in the top 5 for Asia.