I would recommend seeing the pandas first, if that's something you really want to do, since it gets very crowded as the day goes on.
There are two forms of bus transportation (you get both with the bus pass) - one is the bus tour that leaves from the bus station near the entrance of the Zoo, and the other is the Express Bus that stops at 5 different places inside the Zoo, and you can get off and on at whatever stop you want.
Personally, I think I would do the following if you want to minimize walking and maximize sight-seeing:
Go down and see the pandas first - that's all downhill, though there are some stairs depending on which way you go.
Take the moving sidewalk (not far from the pandas) up to the mesa (towards the entrance to Elephant Odyssey, though you won't be going there at this time), and then take the Skyfari BACK to the entrance - the line for that won't be so long in the morning. Before you take the Skyfari back you might want to go a little further down the road and visit Polar Bear Plunge - if it's open at the time you go. You could also take the Express Bus back instead of the Skyfari, but it'll take longer (more stops).
Then walk back to the bus station and take the bus tour.
It's still a fair bit of walking, but you'll avoid walking the hills for the most part.
After the bus tour, you can use the Express Bus to go back to other areas you might want to see more closely - like Elephant Odyssey - you really don't experience that at all from the bus. And also the koalas.
Here's my Zoo tour strategy - but I don't mind lots of walking and hills.
Enter Zoo, go through Monkey Tail and Forest Trails to the Tiger River Trail, where we see tigers, okapi, hippos, and at the bottom are monkeys and otters. You're at the bottom of the canyon at that point, so then we head towards the pandas and see them.
Then continue along the bottom of the canyon till we get to the path on the side that takes us up to see the big cats - it's just past the entrance to Sun Bear Forest and across from the hornbills. There are various kinds of leopards, mountain lions, jaguars, and lynxes - we also like getting there early since they tend to be awake first thing in the morning instead of sleeping! We walk partway up the hill till we've seen the last cat (lynx) than go back down the other side past the small carnivores like foxes, fossas and coatimundis.
Then we backtrack back past the pandas again and go up the other side of the canyon past the raptors to Polar Bear Plunge (this is a pretty steep uphill sidewalk, though). After Polar Bear Plunge we walk through Elephant Odyssey, and that brings us back up to where we're on the level with the Zoo entrance again, though it's still about .3 miles back to the entrance. But up on that level are the camels, koalas, rhinos and giraffes. Near the entrance are the orangutans and further in are the gorillas.
Past the entrance of the Zoo we'll often go into the Children's Zoo, though mainly all we're interested in there is the nursery - it's fun when they have baby animals in there! The Reptile House and the Wegeforth Bowl are off in that direction too, though we don't do those very often.
There's also Bear Canyon, Fern Canyon, and the aviaries, but birds aren't very interesting to us.
).
