For Yellowstone, you would have to do that from more than a couple base camps, maybe, depending on just what parts of the park you want to see. It is a very large park, with areas that are quite different from each other.
People who want to see more than just the geysers might find themselves driving 40 miles from campground to trailhead, then spending the day hiking 15 to 25 miles. It would be difficult to recommend any particular CG without knowing just what it is that you want to experience.
I would start with buying a guide book. It has been so long since I've gotten one that I don't know what to recommend among the more than 1000 books currently in publication, but you might look for something with "hiking" in the title. My own interests would be rather "geology" and "wildlife."
My Yellowstone experience, I would rather not walk the park roads. Although speeds tend to be slow, drivers are also inattentive to pedestrians and cyclists, while at the same time being in a hurry if there is nothing to see immediately.