Hi Pat (and all),
not sure if you made it here yet, but if you haven't and still need pointers, here are a few.
I live in Jackson, which is just south of Yellowstone and 3 miles out of Grand Teton National Park and I have also
spent a summer working inside Yellowstone.
1) The Old Faithful geyser is in a great location for sunset shots, but the place is really crowded all summer, if you could
make it there in September or October before the park closes you would be able to take better shots.
2) ...better yet, hike Lone Star Geyser, which is just as regular than Old faithful but much less crowded (it's about a 20 minutes
easy hike from Kepler Cascades (also nice place to photograph), the cascade parking lot is about 15 minutes from Old Faithful.
3) Don't miss the Canyon of the Yellowstone with Lower Falls (and lesser extent Upper Falls).
A great hike is the Uncle Tom's Trail which takes you right under Lower Falls and provides a
very dramatic view, it's a lot of steps to get down (worse part is going back up) but totally worth it.
4) Shoshone Lake has it's own geyser basin, it's a long hike and few people go there but a great way to go is paddling
a canoe or kayak from Lewis Lake (south of the park opposite Yellowstone Lake). The company I work for organizes multiple day
trips to Shoshone Lake or you can also rent canoes/kayaks from us and get there on your own (website is: http://www.snakeriverkayak.com
We're open until the end of September.
5) Yellowstone has an unpredictable weather and it's own micro-climate, make sure you have at least
a dry-bag to protect your equipment in case of sudden rain, etc.
6) Hayden Valley and Lamar Valley are the best places to sight grizzlies, having a long range zoom certainly helps.
7) Don't leave home without a tripod and cable release.
Explore Sylvan Pass (8530 ft.), it's the road toward the East Entrance and Cody (lovely town, my favorite in Wyoming).
Great Views from there.
GRAND TETON NATIONAL PARK
Just as great with awesome views.
1) For a beautiful skyline photo, catch the sunset over the Grand Tetons from the hills on Moran Junction.
See photo below from my website (http://www.lucadiana.net
2) Hike the 4.5 miles trail (each way, about 3000 ft. elevation gain) from Lupine Meadows to Amphitheater Lake
(Strenuous, Park Services gives an average of 8 hours for a round trip, although I have done it in little over 2 1/2).
The hike takes you to glacial lakes (Surprise and Amphiteater) surrounded by sub-alpine meadows.
3) Take the easy hike from South Jenny Lake to Hidden Falls (about 45 minutes each way), make sure you have your tripod.
Best time to see the falls is in May/early June when they are huge. After most of the snow has melted.
4) Buy the National Geographic trail map of GTNP (best spent $9 in the park) with all the hikes and details.
Map #202 if I recall correctly.
5) At this altitude a polarizer is a must. But the morning light is harsh since the start. The best photos I've seen
were taken between 8 and 10am when the colors are nicely saturated.
6) ALWAYS bring lots of water with you and some snack like trailmix.
I hope this helps for a start, if something else comes up I will add it here.
PS: Lots of tourists refer incorrectly to the town as Jackson Hole. The name of the town is Jackson. Jackson Hole is the name
of the Valley that runs for about 60 miles from south of Yellowstone to south of town and includes also Teton Village
(the famouse Jackson Hole Ski Resort).