I hope you enjoy your trip to Sydney! I would second
@Zoofan15's points. As he indicated, Taronga Zoo is centrally located to the Sydney CBD, just across the harbour on the ferry (or the 100 bus from Town Hall, albeit via a less aesthetic journey). If you want to see ABC zoo animals, go to Sydney Zoo, but Taronga Zoo is the more iconic due to its harbour location.
In relation to navigating the slope at Taronga, I would recommend zig-zagging across the map (so you do everything on one particular 'level' of the hill before heading down to the next), or going down the giraffes/tigers side first, then coming back up the hill on the Australian animal side, as the hill seems less pronounced.
That said, if you're arriving on the ferry, there's the opportunity to enter the zoo at the bottom, which may be a good idea as you tackle the hill more gradually (stopping at exhibits and so forth), then at the end of the day, all you need to do is walk downhill in order to get back to the ferry. There is a public bus which can take you to the top as well, which helps.
Sydney Zoo is not really located near other tourist attractions, although is very close to Featherdale Wildlife Park. It may not be an option for you, but you can relatively easily do both in a day (as I have often done), so that could be an opportunity for you to visit more facilities if you would like to.