Watarrka National Park is on the circuit travelled by people wandering about the Red Centre. South of Alice Springs, north of Uluru and west of the Stuart Highway. It's a bit of a detour off the Stuart Highway if you are heading south, but, if you're on the Stuart Highway around these parts, you are probably as close as you are going to get.
The park itself is in the George Gill Range and encompasses a number of dry creeks as well as a few permanent waterholes. The main tourist area is around Kings Canyon and seems to see a half dozen (or more) tourist buses driving through each day. I'm not sure what you see of Kings Canyon if you have only a 20 minute stop from a tour bus as the park is best experienced on one of the longer walks.
There's an amazing corner crack in there
As you enter Watarrka National Park from the east, you pass first Kathleen Springs. The Giles track (22 km one way) ends here and there is also a short (2.4 km return) paved (wheelchair accessible) walk up to the waterhole at Kathleen Springs. You get a bit of a sense of the sandstone pagodas in this area from the Kathleen Springs track which is a pleasant half hour wander.
Another 40 km further west is the main Kings Canyon area where the other end of the Giles Track starts and a 6 km (8 km with side trips) loop walk leads up from Kings Creek onto the plateau top and wanders along sandstone pavements between sandstone pagodas around the head of Kings Canyon. This is a really nice walk that is pleasant to amble along taking in all three of the different side trips - the first up King Creek to a low viewing platform, the second out to the canyon rim above a superb splitter crack, and the third to a waterhole and dry waterfall at the eastern end of Kings Canyon.
Doug walking among the sandstone pagodas
Unfortunately, like so many places around the Red Centre climbing is banned. The sandstone is hard and patched over with desert varnish plates. If you've climbed in Red Rocks, it all looks very familiar and you really, really, really want to go climbing, but you can't.
The Giles Track runs between Kings Canyon and Kathleen Springs and intermittently wanders around sandstone pagodas, up and down into dry creek beds fringed with river red gums, and through brilliantly coloured wildflowers scattered amongst mulga forest. Its a really nice day walk, quite easy as there is very little elevation gain, and not too stony and hard on the feet. I walked from Kings Canyon to Kathleen Springs while Doug (who has some knee and foot issues) walked half the distance from Lila spur to Kings Canyon. If Kings Canyon is too busy with walkers, you'll be presently surprised on this track as I met no-one but Doug (walking in the opposite direction) all day.