Best place to stay at Kings Canyon

I agree that the resprt van park is a good choice.
You can get an unpowered site if preferred.
For my money, I would spend more time at the canyon and much, much less at Uluru.

Last year, we did the Kings Canyon/Uluru "thing".
The Resort was almost empty, but the sites were all filled aeemingly by design, from the central area outwards. AND there were a heap of school buses there, all in and around the central area.
Would have been SOOO much easier to have allocated van sites closer to the outer edges (and there were plenty of facilities further out!) rather than all clustered around the bus/kids tent sites. The kids were noisy, but the most difficult thing was that the bus parked no more than 10 metres from our van was planning a 5am departure so the kids could "do" the rim walk. Try to keep a coachload of kids quiet at that time of day? Did OK, but still woke us far earlier than we wanted!
Trouble at the Uluru campground was that a coach of kids (not the same ones as at KC) contracted gastric, so one (of 2) facilities units was closed to the public. That caused a bit of a hiccup! They need to get more facilities blocks built for use by vans, for mine!

The Creek has the bus camps in a different area to the other campers. They also have their kitchen shelters with the bus camps.

I second the Station. Stayed there 2012 and really enjoyed the atmosphere of an outback station. Travelled to KC and did the rim walk.
A truly magnificent place.

"The resort will probably mean 60km less driving,"

If you don't go any near the the resort it is 12 km less driving. You have to come back 6 km from the Resort to the turn off.

If you stay at the Creek you will have 39 km less van towing. You only need one day at the canyon. If you want a second full day in the area there is another feature half way between the Creek and the gorge.

Map showing turn off points.