Best days to get a campsite without reservations is Sunday thru Wednesday, early. Trying to hit one on Thursday or Friday would be much more chancy.
I don't normally do reservations. But if I had a 30' TT, 4 kids, and a limited time window, maybe I would do them for a park as busy as Yellowstone.
I like the advice about starting early each day and being back at the campsite by about 6pm. Personally, I don't like crowds so Teton NP is more my speed; one can be much more laid-back about the camping and driving around the Tetons.
