I have spent the summers of the last 8 years visiting Yellowstone and nearby environment. Dealing with the last first, I would recommend that you take a day and do the Beartooth Highway just outside the North Entrance of Yellowstone; arguably the most beautiful highway in US. Car only is recommended or if tough a motorcycle. Also, give consideration to a couple of days at Cody to see the really sophisticated western museums and then enter Yellowstone from East Or come from South through Tetons.
I stay at Yellowstone Edge - 35 miles North of North Entrance on US Highway 89 in what is called Paradise Valley and it is in fact. The 30 minute drive to Yellowstone is in itself great viewing with, dependent upon time of day and weather, fields full of Elk, Antelope, Mountain Goats, Sheep and speculator mountains as well. The scenery at YE RV park is great and its location right next to the Yellowstone River makes for relaxing evening. A community gathering around a campfire occurs every night at 7PM. One can see much of this park by going to mtrv.com and then clicking on camera link; the camera is very good (actually has been purposefully downgraded a little to add some privacy) and one can control to see all surrounding area and even the folks around the campfire. One can go to Livingston 20 miles away for some excellent dining and museums. Also, there are a couple of excellent restaurants near the campground.
Inside park, a 20 year construction project makes for delays but not nearly as bad as tourists who fail to follow orders and block roads or refuse to follow park patrol directions when sighting a bear , bison or Elk or who fail to pull off into byways to allow faster traffic to proceed. So, patience is a great virtue in the heavy tourist months of mid-June to mid-August. In my Yellowstone presentations during winter in East to RV clubs I point out that Yellowstone is a revolving panorama. The time of day, the day of month, the weather and other factors determine what you see. You can not SEE Yellowstone in a day, week, month. As an example, I have never seen in 7 years, Elk or Bison on the land between the North gate and the Arch. I got here early this year (April) and both were on the land in large numbers. I'm not sure it had to do with earlier visit or the unusual weather we had this year with late snow and cold wet weather. This is one of the nicest years in terms of green fields in mid-August. The summer rains have had a major positive impact. Its also my impression that bear sightings are far more frequent this year; all most becoming commonplace.