Thanks to everyone for your remarks. I've come a long way up my learning curve since posting, thanks to you, a couple emails, and a very helpful phone conversation with ranles (who, btw, strongly endorses Cooper Peedy as being even more interesting than Alice Springs or Ayers Rock.)

I've decided on a bit of "If it's Tuesday, it must be Belgium" sightseeing.

I've changed my ticket to fly directly into Ayers Rock. I arrive at 11:30am. I'm going to stay at Lost Camel, the cheapest hotel that is offered - and still very expensive as a single traveler. I've booked the Sounds of Silence dinner. I'll have 24 hours to see both the Rock and Kata Tjuta.

Then I'll take the afternoon bus to Alice Springs. This will give me a chance to see the desert scenery. I'll stay the night in Alice Springs, and have the morning there before an afternoon flight to Sydney. I'm still debating as to whether to tack on a day here.

I'm happy. I think it's a good compromise.