Another option for seeing Lake Eyre is from Level Post Bay via Muloorina Station. You turn right off the Oodnadatta Track a couple of km out of Marree, then head North along the graded road from there.
Campsites are spread out under trees beside the Muloorina Waterhole on the Frome river. There are flush toilets, but no showers, and you need to bring your own water.
There is a lot of birdlife here, and also a natural artesian bore water 'pool'. It's like a little dam with a silty bottom (nothing flash like at Coward Springs or Mungerannie) but it is soothing.
It's a nice drive from here up to Lake Eyre, passing Lake Eyre South along the way.
Muloorina Station asks for a donation for the RFDS as your camping fee, and there's a self registration/donation box as you drive in. We stayed here because we were travelling with our dog, and couldn't access Lake Eyre from the William Creek side with her. It is NP at the Lake edge on this side too, but we were able to keep her in the carpark while we walked the 50m or so to see Lake Eyre.
Like everyone else has mentioned, Coward Springs is a favourite. It's a little oasis along the track and the kids will love it.
Have a great trip!
Cheers
Karen
Here are a few photos of Muloorina:
The road in
Our campsite
The main waterhole
The hot spring