Starting near the entrance: the aviaries outside the Elephant House are not to easy to shoot - but the Derbyan parakeets are beautiful subjects. I've never tried with the hornbill indoors.
Check the condors when you're at the top of the bridge to the East Zoo; they sometimes sit on convenient perches, but the aviary is so big that you need a long lens.
Islands in Danger is worth a look, you rarely see the red birds of paradise in good poses, but you can strike lucky with Tarictic hornbills or Palawan peacock pheasants. Naturally all the indoor aviaries have poorer light than the outdoor ones. I find it difficult to shoot the free-flying birds in the Topical House, stake out the feeding trays etc near the crocodiles if you want to try. The hornbills in the lower aviaries are possible, the birds in the upper row of aviaries are smaller and more skittish, but the light is better. The aviaries near the entrance and exit of the Tropical House are hard to shoot, as are the pair of aviaries in the picnic lawn.
I find the aviaries in RotRA are difficult - although the birds are very attractive, but go early or late as the house can get very crowded.
Don't forget the penguins or the flamingoes, and don't forget the aviaries behind the shrubbery across the path from the otters. The Chinese species (laughing thrushes, monals, Peking robins etc) are real challenges, but the young pair of rhinoceros hornbills are very worthwhile subjects.
Europe on the Edge is one of the best places for photography and there are plenty of nice subjects.
I often find that one of the owls or tawny frogmouths is posing nicely, and you might be lucky with the lilacine amazons in the parrot breeding centre (they are the only birds on show). The only other birds at that end of the zoo are the Manchurian cranes, the cassowaries and the red-billed blue magpies (beside the lions).
In the West Zoo, you can shoot the waterfowl from the hide opposite the dikdiks, if the birds come close enough. The Stanley and wattled cranes are in paddocks below the Tsavo Aviary. The Tsavo Aviary is one of the best places for shooting birds, but if the sun is shining they are mostly against the light, I prefer to shoot there on slightly cloudy days or late in the day. You have to be patient to see all the species, but it's worth spending time there just watching the weavers and keeping an eye open for the robin chat etc.
Hope this helps.
Alan