Both locations are fantastic for landscape and wildlife.
For Grand Teton, I'd recommend the following for good landscape opportunities in the morning:
1. Mormon Row--there are some old barns from when the land was acquired by the government. These make a good foreground subject against the mountain backdrops.
2. Schwabacher landing--this was my favorite location. There is a beaver dam that creates a nice pool that will give you excellent opportunities for getting good reflection shots of the mountains.
3. Snake River overlook--if you're familiar with Ansel Adams' work, this needs little introduction. It is different than what you see in his famous shot as the trees have grown taller, but it still is a great view.
4. Oxbow bend--great location for birds (osprey and bald eagles) and potentially moose. This is another good location for getting reflections of the mountains.
The Cascade Canyon trail will give you good opportunities for spotting wildlife (moose, elk, bears, etc.).
For Yellowstone, there are many unique locations. For wildlife, I'd suggest Hayden valley and the Lamar valley as there are many elk herds. There are also active wolf packs that are in these areas, but you will need to be patient (and a little lucky) to spot them. Dusk and dawn will be the best times to see wildlife on the move.
One of my favorite spots is near the top of a bluff just to the south of Grand Prismatic Spring. The boardwalk near the spring itself is worthwhile, but if you park at the Fairy Falls parking area (southeast of the parking lot near the Grand parking lot), then you can walk on a path that flanks the bluff to the north. Once you are in line with the spring, you can climb the bluff to get excellent views of the spring. It is a bit of a scramble and beware that you are not going to be on a trail while doing this. However, if you are careful, you will be rewarded with excellent photo opportunities.
Many people will advise you to go to Old Faithful. It is worth seeing, but if you are willing to wait, Grand Geyser is much more impressive. If it is late in the day, then you can get the pleasing warm side lighting and a rainbow from the geyser mist.
Another must-see is the Grand Canyon of the Yellowstone. The canyon is impressive (not like the Grand, but still very worthwhile). A popular place to shoot photos of the lower falls (the larger of the two) is at Artist's point. It will give you a view of the canyon a fair distance from the waterfall. You can also spot several osprey nests along the canyon walls.
Mammoth hot springs and terraces are also worth visiting if you have the time. Happy shooting.