[font color=\'#000000\']I love Yellowstone, but it is a long way from England and there are many other great places to visit. I am not a wildlife photographer and my comments are biased to landscape. However, common wildlife (bison, elk, coyote) are everywhere. From my experience, these are some good locations to start with:
Artist Point for view of Lower Falls, a classic viewpoint, probably the most visited but no less spectacular for that, best in overcast conditions since sunshine can give contrast problems.
Alum Creek, Hayden Valley. Best pre-dawn for mist on river and fantastic sunrises.
West Thumb Basin. Interesting but maybe not spectacular
The main terrace has dried up over the last decade although Canary Spring still has some nice shapes and colours. Best early morning since in shadow at dawn.
Road from Mammoth south to Norris. Very atmospheric dawn to early morning
Around Old Faithful
If you are limited in time, base yourself here. If you can stay at the Inn all the better. All of the Upper Geyser basin is worth investigating. You should see Old Faithful going off but don't expect exceptional photographs. Morning Glory is my personal favourite but difficult to photograph due to proximity of boardwalk and messy background.
Best trip is to Firehole Lake Drive and Tangle Creek. You'll run out of film if you have a bright dawn with frost about!
Grand Prismatic Spring is also a favourite of mine. You may be lucky with nice shapes to the runoff, but the spring has been drying out over the last few years. Strangely, the mist over the spring gets much denser just after dawn and you can't see a thing!
Clepsydra geyser is a fine place to visit for sunsets
Slightly further afield, towards West Yellowstone you may be lucky and see a bison herd crossing the river. They do this quite regularly at any time of day.
Whatever you decide, don't try to do too much. Yellowstone Park is huge. Enjoy!