The best time of the year for going on a self-drive safari is the next two-three months. It's dry season, so not too much green for the animals to hide in. (Some animals still manage to hide just fine, though, as seen here.) And there's no mosquitoes to worry about until the rains begin, so no malaria either.

There's a fairly high entrance fee for the park per day for foreign visitors, but if you buy an "annual pass" (the Wild Card), after a week you're there "for free" for as long as you want. And it's really, really easy to spend two or even three weeks just driving around in this huge park, staying in a different camp every night.