Well, of course the safari, Festival of the Lion King, the two walks (Maharajah Jungle Trek in Asia and Pangani Forest Exploration Trail), Kali River Rapids if it's hot, Expedition Everest if you like thrill rides. Honestly there's nothing there I skip except Nemo (and that's more circumstances than because I don't want to see it). But to me "walking around and looking at things" is the best thing about it. Besides the animals mentioned above on the walks, make sure you see the macaws, the gibbons and siamangs, the lemurs, the otters (man, I could watch tme all day), the cavy, the babirusa ... they have both types of kangaroos, although the grey ones were off display when we were there. Try to guess the theme of each building in Discovery Island (things like "animals with spots and stripes") and in each room of Pizzafari. Look at the tree from as many angles as you can and see how many animals you can find.
The best trail, according to our Wild by Design tour guide (and we agreed after we did it) is if you go behind the tattoo cart opposite the baby care center and make your way towards the tree from there. It exists near the entrance to It's Tough to Be a Bug, at the lemurs.