Alice Springs is the best place to start your campervan hire if you want to visit Ulhuru (Ayers Rock).
It is about 6 hours drive along the Lasseter Highway. You need to allow plenty of time and only drive during daylight hours. There are campsites at Uluru but you need to get there early in the winter months as it is a very popular destination for campervannners.
The climate is dry and arid. It does rain in the winter months so the best time to visit is in April.
Australia.com publish a great "Red Centre Way" driving route. Red Centre Way Driving Route between Alice Springs and Uluru.
There is the full range of campervans, motorhomes and 4x4 campers to hire. You may need the 4x4 if you intend to go off the main access roads.
Alice Springs is in the heart of the "Red Centre" so there is plenty to do and see. Take your camper to most of the main highlights such as trekking the rim of Kings Canyon and experience the gorges of Watarrka National Park
Visit Ulhuru but don't forget the yearly Camel Cup! You need to book ahead! Add Kings Canyon which is southwest of Alice.
There are plenty of campsites around.Alice Springs Campsites