I went there back in 1991 - budgeted a week's stay in Alice and side trips to Uluru and Kings Canyon - both were mindboggling and a week wasn't long enough. If going, do it properly. Either fly or drive there, and reckon on spending at least 10 days seeing things in the area. There's a lot to see. Some crazy good museums and art galleries too. If driving, take a 4wd or a VW Kombi - the roads are NOT good. I went in September, after the first fall of rain in several years. The wildflowers were off the planet incredible.