Steph and I were there this past July for our honeymoon. Two things thas suprised us were how empty the park was, and how cold it was. The weather was storming on us the day we were there, but we got lucky and were able to see the basics between thunderstorms. We sat in my truck for half an hour waiting for the rain to stop at the falls, but it was jsut partly cloudy when we were at Old Faithful. We couldn't see the Tetons in Jackson, but when we were in the park, it cleared up and we were able to get some amazing pictures.
We spent the day driving all over the place and only saw a few dozen elk and not one single bison!!! We saw more mule deer on that day then in all my trips there before combined!! No bears, moose or wolves.
If you have the time, three days is plenty. The sites are all something you can see in one day if you try, but two days will make it easy on you. To find all the animals, you need to ask around and stop at all the traffic jams. When animals are spotted, people pull over on the side of the road and get pictures.
Steph had never seen a moose and that was something we really wanted to find, but when we asked others, we learned that all the moose sightings were back in the Tetons and nobody was seeing in Yellowstone that day. We didn't have time to go back to look for moose, so we never saw one.
With three days, you should be able to find the animals and see the sites.
A few years ago, I stayed at Fishing Bridge RV Park. It was ok, but there were very few animals there. We drove to Madison every day to see the big bull elk and allot more animals. There was a heard of several dozen elk right beside Madison RV Park with several massive bulls. Of course, there's never a gurantee where you will find the animals, but with a few days, you will see them.
Be sure to go out the North Entrance and to the town of Gardner. There is a sporting goods store that sells wildlife and hunting vidoes made by Gordon Eastman. He was fairly famous for his videos back in the 60's and 70's. The guy who owns the place was his business partner and he knows the park and area better than the rangers do. He had a spotting scope in his shope and showed us two heards of bighorn sheep. He told me how to get up close to them, which we did, and I had the greatest time taking pictures of some huge bighorn sheep at just one hundred yards.
One disapointment that I found when we were there was that the Mammoth Hot Springs have just about stoped flowing and the calcium deposits are falling apart. They were very unique and something I really wanted to show Steph.
On your way to Yellowstone, be sure to go to the Black Hills in South Dakota. If I had a choice between the Black Hills or Yellowstone, I'd go to the Black Hills. For me, it's not even close!!! You can stay in Custer State Park, go to Wind Cave State Park, explore several caverns, see Mt Rushmore, Crazey Horse and the town of Deadwood. There are so many things to do there that a week wouldn't be enough!!!!
Just a short distance from the Black Hills, and kind of on your way to Yellowstone is Devils Tower. It was the focal point of the movie "Close Encounters of a third kind." It is this countries first National Monument and definatley worth seeing.
Then just before you get to Yellowstone, go to Cody Wyoming. The Buffalo Bill Cody Museum is there, and it's probably one of very few museums in the country that rival the Smithsonium. It's that good!!! Also in Cody is a collection of log homes and buildings from all over the old west. The owner bought them, dismanteld them and reasemebled them there. One salloon has the bullet holes in the walls from the Sundance Kid!!! It's just something that's very unique and interesting in one place.
A good website to read up on these places and traveling is
RV.Net : RV Accessories, Supplies, Classifieds, Insurance, Financing & More They have a site similar to here, but focused on RV's, places to stay and what to do there. Lots of good information and helpful people. If I was you, I'd join that sight and ask for suggestions just like you did here.
Another very good thing to do is go to each states website you will be going through and request there tourist guides. They take about a month to get to you, but they are free and full of everything there is to do in there states. The one for South Dakota is a MUST!!!!
Have fun!!
Eddie