It depends what sort of wildlife you are interested in and often the time of year is critical for wildlife viewing.
April is also the perfect time for tigers in India. The high temperatures mean the tigers need to find water. A train or car from either Mumbai or Delhi will take you into the heart of Madhya Pradesh.
It's certainly not my best experience in terms of wildlife viewing but sadly I think that's a tigers plight.
Madagascar is a connection from JNB as well albeit a bit further away. No lions, giraffe or zebra like the film but incredible nonetheless.