We are looking at visiting for 2 nights in April. We can stay in the right on the rim for $191/night which makes me cringe. We can stay a 15 minute walk for $125/night. We have 2 kids so google tells me it's worth it to pay the extra to stay closer to the action. But the extra $65/night is pretty significant.
We stayed in Mather Campground in June, and it was fine. There is a bus system that makes getting around pretty easy. You'll be walking/busing farther to see the different lookout points than you will to get right from where you're staying to the rim (assuming it's really a 15 min walk).
Unless you value (and are willing to pay for) having canyon views from your window, I think you will be fine with the location of Yavapai. It's very central, the camp store is there if you need anything, etc. The rim is very close, as are bus stops. The campground we stayed in was twice as far from the rim, and it was no biggie (although we didn't have kids).
As far as how nice they are relative to one another I have no comment obviously, but they are all run by Xanterra so I imagine they are pretty similar.
We stayed at Yavapai lodge and it was great! Walking distance to the "general store" and cafe. I assume you will have a car - it is very easy to drive around. We were only in the room to sleep...very clean, nice earth friendly bath supplies, depending on when you go though, only certain rooms have AC..