Three days at Yellowstone worked fine for us. And we spent our time at the attractions and did some hiking.
We did not stay in the park as I felt it was a bit too crowded for our camping style. I got a beautiful site across the boarder at Henry's Lake State Park in Idaho. It was about a 20 mile drive from the Park to Yellowstone. In exchange we had a large peaceful camping site, electricity, a premier fishing lake, and no worries about bears (we were in a popup at the time). In fact, while Yellowstone was really neat, I found sitting around a campfire, clean air, zero noise-pollution, incredible stars at night, and the total lack of stress at Henry's Lake pretty awesome!