Depends on what you like to do.. here's a variety of things a friend of mine did on his visit out there last year:
Alice Springs Desert Park
Old Ghan Museum
Alice Springs Cultural Precinct
Royal Flying Doctor Service
School of the Air
Also you should take a tour with Frontier Camel Tours for something different.
Hope this helps! almost 10 years ago
I assume you are going to Uluru/Ayers Rock and Kata Tjuta/The Olgas as part of this trip.
In Alice Sprints:
You could spend half a day / full day at Alice Springs Desert Park.
The Telegraph Station is also well worth a visit.
The School of the Air and Royal Flying Doctor Service are good to drop in to briefly.
If you have a car, drive out to the East Macdonnell ranges and have a look at some of the 'gaps' and gorges - they are beautiful. Make sure you have enough petrol though (I didn't have much to start with and almost ran out -- no mobile phone reception here)
Glen Helen (West Macdonnell Ranges)
From Alice Springs - there are some trips that you can do - one of them goes to Glen Helen on the West Macdonnell Ranges (west of Alice Springs). From memory it was a 2 day trip and this was the best part of the trip that I did. We came back via Hermannsburg (an aboriginal old settlement / mission that was set up).
We also did a day trip into The Simpson Desert from here -- to see Chambers Pillar and Rainbow Valley - absolutely spectacular. You need to go on a tour here and can't do it yourself.
It is an awesome place to visit!!
Enjoy. almost 10 years ago