Enicalyth, that was about as close as it gets!
About the only thing I could ever hope to add to what has been written is that if you did get the opportunity and are flying yourself (which if you could there is a lot to more to see than the average tourist ever gets to see - especially in the Western Macs, Gosses Bluff crater and Ormiston Pound etc etc etc are fantastic from the air in a lightie), then if Uluru/Ayers Rock is your fancy and you are on a budget then why not stay at Curtin Springs? It is about 45nm east of The Rock, has a 1400m strip (albeit gravel) and the accomodation ranges from free camping to a/cond rooms (what are referred to locally as "dongas") that are reasonably neat and presentable. The family owned Property is a working cattle station with a store/pub etc and a stop off point for busses, backpackers and tourists of all kinds and descriptions so a broad cross section of Australia is the go. I was lucky enough to live there a few years ago now and was the station pilot at the time. All in all I spent about three years in The Centre.
While many only think of Central Australia as The Rock, the Olgas and Kings Canyon and a whole heap of red sand, that is but the tip of the "iceberg" so to speak. If you can't hire an aircraft yourself, then fly the fam to Alice on the 'burner, then when you get there look up a bloke who posts here under the name "Bushy". He has the good oil on tours at the right price to see what there is to see to get a feel for the place.