Hi L8r,
We lived in Alice Springs for 5 years before moving to Tasmania 15 years ago, and were more into 4wd car camping then rather than bushwalking as such, with a lot of exploring of the gaps, gorges and chasms etc.
I'd suggest Glen Helen Gorge, Ormiston Gorge and Stanley Chasm along the Western MacDonnell ranges as 'must see', with permanent waterholes perfect for swimming (which was a popular constant while we were up there

)
Kings Canyon is a spectacular place with a fantastic circuit walk that takes you to the top of the canyon, if you get time to go out there.
I'ts a dry heat there, which I prefer to humid heat. Apart from protecting yourself from the sun by the usual means, and walking early and late, there is not much you can do to avoid it if you want to enjoy the outdoors. Try draping a wet handtowel around your neck.
I dont know much about the Larapinta Trail (there's a thread here somewhere), but you could pick it up at one of the Gorges and go for a wander along it for a while and then return.
Thanks for bringing back the memories.
Geoskid