We saw moose along the Madison river on the West side of the park and along the Snake river going to Jackson Hole. I hear the wolves have damaged the moose population severely. If you want to really experience Yellowstone, get out of the car and do some hiking on the trails into the backcountry. The last trip we made there, we hiked into the Pelican Valley. About a mile from the car we found a fresh bison pile with a huge grizzly hind footprint in the middle of it. Talk about the hair standing up on the back of your neck! You will never be more aware of your surroundings than at a time like that!
Probably less than 10 % of Yellowstone visitors venture more than a few yards from the roads or parking lots. A lot is missed because of that. It's a humbling experience to know you are not at the top of the food chain! Either way you will have a great trip!