Having visited Vienna barely 2 weeks ago, I feel like I can give a decent overview for the zoo.
Starting from the Neptune entrance, there's a large paddock for Indian rhinoceros, nilgai, Vietnamese sika deer and blackbuck. For Indian rhinoceroses, this is possibly the best enclosure I've seen in any city zoo, maybe ever.
The Rainforest House has mostly Asian/Indonesian species so I'm not entirely sure what species count here - but most occur west of the Wallace line as well. Highlights here are huge amounts of Oriental white-eye and blue-crowned hanging-parrot, but also northern river terrapin, rock frogs (Staurois parvus and guttatus), 2 flying fox species and orange-bellied leafbirds. Important here is the incredible work Vienna has done with the two Staurois species - they were the first to import them to zoos, and to breed them too. IIRC they do some in-situ conservation with the terrapins too, but I don't recall what exactly.
Amur tigers and Amur leopards have a large aviary, which looked well-planted. We didn't take a good look at the outside enclosure because they're pretty common so maybe someone can confirm that these enclosures are indeed appropriate for these species?
Giant pandas have what is possibly the best outdoor enclosure I've ever seen for them. Lots of foliage and climbing space.
The Aquarium-Terrarium House has few Asian species, but I saw Chinese crocodile lizards, tentacled snakes and spectacled cobra.
There's a few other Asian species throughout the zoo - Himalayan tahr, lar gibbon and Sumatran orangutan most notably, all in good-to-great exhibits.
The Desert House outside the zoo contains Kaiser's newts and long-eared hedgehog, but both of these are kept in a rather barebones enclosure. (Does this count for the challenge? It costs extra to enter but is jointly managed by the Tiergarten and the Schönbrunn park botanical department)