Short of buying a book or two I can give you some ideas...
First, June begins the peak season and travel in the park can be difficult due to the higher number of people and vehicles.
Second, depending on the amount of time you have you should plan on driving most of the main roads as there lots to see all around Yellowstone, but it's not unlikely that some of the roads, particularly in the NE, may not be open due to snow.
Third, while the popular places like Old Faithful are likely to me the most crouded places you'll still want to go there. Can't go to Yellowstone and not visit Old Faithful can we! Also, there are lots of nice things to see and shoot along the walkways that procede north from OF.
Forth, at the north entrance or Mammoth, there is an area of hot springs that can have very colorful pools of water in addition to the interesting formations. Also a good place to stop for lunch.
Lastly, you will see plenty of wildlife wherever you go with Bison and Coyote being a couple of the more common critters. Harder to find are the bears, black and brown, but if you are there more than a few days and get to the northern parts of the park you should see some bears, maybe even a mother with cubs. Be caeful to not get too close. As for Wolves ... the best place to see then in in the NE part of the park in an area called Lamar Valley. The only problem is that you are unlikely to get very close to them as then dens I've seen are at least a half mile from the road. Still you can get lucky -- a couple years ago I was there and waited for several hours atop a hillside overlooking the valley, a place you're likely to see many people with scopes and big lenses looking from. But, after a few hours of nothing I left and was heading to one of the turnout parking areas about a half mile further east and as I got about half way there I saw a bunch of flashes from cameras. When I arrived at the spot I was informed that a wolf had just crossed the road not 100 feet from the parking area. Pain of it all was that I missed it by maybe a minute.
Oh, and one more thing ... perhaps the best place to stay is in West Yellowstone at the western side of the park. You'll be about 30 miles from OF and at the western center of the park. Check out this link for the following:http://www.nps.gov/archive/yell/interactivemap/index.htm
Notice at the east side near a place called Canyon, is an area with a beautiful waterfall and a river gorge with very colorful soils.