I love arriving at AK early and heading right to the safari. I also really like to visit in the afternoon. The experience is very different. The tigers on the trail in Asia are most active after 3PM. They often play together, walk, swim and pace around in anticipation of dinner time around 5.
Many people line up early for the parade which begins and ends in Africa around 4. Right after the parade passes, you can often hop on the safari with little or no wait. On a hot afternoon, the animals may not be very active. Other attractions often have short lines during the parade.
At the Rafiki's Planet Watch, they have interesting animal shows from around 11:30 to 2:30. They display animals you won't see elsewhere in the park, like an Asian Porcupine or a lesser anteater (Tamandua).
Many animals will likely go off display at the normal time even if the park stays open late. The extra evening hours would be the best time to experience the attractions in Dinoland and see Its Tough to be a Bug. The lines for these two attractions can get long in the afternoon, but both often have fastpasses available.