I was up at Grand Teton/Yellowstone about two weeks ago. Wildflowers
were still blooming. I've always found Grand Teton to be far more scenic
than Yellowstone. Leaving Jackson going north on 191, there will be a
pull out at the Nat'l Elk Refuge, there's a big pond there, stop and see
if there are any swans in it. In Grand Teton for early morning
shots...Mormon Row, you want to be there right at sunrise for the best
photos. As you come in from the south end of Grand Teton, turn right
onto Antelope Flats Road, you'll see the houses on your right, you'll
have to park and walk a bit, the road is chained off. Get back in the
car and turn around to follow the Mormon Row road south, there's another
barn down there. You may also find buffalo in this area. Back on the
main road, further north after going through the park entrance at Moran
is Oxbow Bend, this is another spot that's really only good early
morning. Also on the main road after Antelope Flats and before Moran is
a turn off for a dirt road to Schwabacher Landing. Follow this one to
the Lower Landing and photograph the Tetons reflected in the river.
Chapel of the Transfiguration is another morning shot, on the other side
of the park, but not early AM, it takes a bit for the sun to clear a
hill and light it. You may see elk on this side of the park. The Chapel
is at the south end of the park just past the Moose entrance station. If
there is no wedding going on, go inside and shoot the Tetons through a
huge picture window. From the town of Moose inside the park, there is a
road that runs to Wilson, not surprisingly, it's named the Moose-Wilson
Road. This is a very narrow but mostly paved road that runs along some
marshy areas. It's a good place to look for moose. It'll end at Hwy 22,
I believe, it's the Teton Pass highway anyway, turn left at the stop
light to return to Jackson.

In Yellowstone, there are of course geothermal features galore. If
you've never been before, you'll want to see Old Faithful on the west
side of the lower loop, there will be a sign stating when the next
eruption is due. If it's going to be a while, take the boardwalk and
look at all of the other stuff in this basin. The Morning Glory pool is
at the end of the walk. Back on the road, you'll also want to stop at
Kepler Cascade, maybe if you get there early enough you can get a decent
photo. I've never got a good one of it because they have a wooden
balcony for the overlook and every time I've been there somebody has
stepped onto the thing causing my tripod to jiggle. Artist's Paint pots
are cool. Dragon's Mouth (or maybe it's Breath, don't remember now) is
also pretty cool. All along both sides of the lower loop you're likely
to find elk, deer and buffalo. I've seen a bear there. On the east side
of the lower loop, you'll want to see Artist's Point, the Lower Falls of
the Yellowstone, Hayden Meadow. There may be bear around the Fishing
bridge area.

Usually, if you're going to do the whole park, you do a figure 8. You
can't do this right now, they've got Canyon to Tower closed to replace
the road. I've never found this particular stretch of road to be
particularly nice though, so you probably won't be missing much. On the
upper loop, you'll want to see Mammoth Hot Springs, there's quite often
elk in this area.

Mt. Rushmore I've not been to, however I have read that you need to be
there at the crack of dawn to get good photos of the mountain. If you
are going to be passing through Moorcroft, WY, you might want to add
Devil's Tower Nat'l Monument to the itinerary. This is the formation
that you will recognize from the movie "Close Encounters of the Third
Kind". You might want to consider buying the year long National Park
pass as well instead of paying at each park. The year long pass is $50
and is good for an entire 12 months. GT/YNP's regular 3 day (I think, it
may be good for 5 days) pass is $20, most other NP's are $10. If you did
GTNP, YNP, Devil's Tower, Mt Rushmore and Badlands, the $50 is covered
plus you'll still have a pass that's good for the rest of the year
anywhere else. If you want to see the maps that you will receive as you
enter each park:
http://data2.itc.nps.gov/parksearch/atoz.cfm
Click on the park. Click on the Plan Your Trip link. Click on Maps.
Download the PDF maps, these are exactly what you get when you enter the
parks.

The first suggestion is get camp ground reservations in Yellowstone if you
can.

One thing you might not expect but probably will have is snow.  It was a big
snow year this year and a cold spring, so I suspect you will still find snow
on trails in the Tetons.  Here are some suggestions:

Tetons:  The classic shots are of the mountains reflected in Jenny Lake or
Jackson Lake.  Early AM is best for sun and still water.  There are trails
around Jenny Lake and it's not hard to find places to set up.  There are
also some spots along the road where you can put the Snake river in the
foreground.  Hiking into one of the canyons will probably give you good
wildflowers this time of year, but check on snow.  Don't expect to see a lot
of large animals in the Tetons

Yellowstone:  You can't miss the buffalo, deer, and elk in the park, but the
big meadows like the Hayden valley on the east and along the road between
Norris and Mammouth on the west are good spots to look.  Bear encounters are
mainly chance.  If you come across lots of stopped cars odds are it's a
bear, and odds are good it's a long way off so bring long lenses and tripod,
and with all large animals think safety first.  (More people are injured by
buffalo which you can easily get too close to than bears, which generally
keep their distance.)  As a general rule if you want to avoid crowds all you
have to do is get off the asphalt.  In the Old Faithful area, check at the
ranger station for geyser eruption predictions.  There are half a dozen
large geysers that are reasonably predictable and if you have a day or two
and some luck you can see them all.  Early AM and sunset are great times for
geyser photos because the warm light and long shadows set off the
"geyserite" deposits around them.  If you have time, climb the Old Faithful
lookout (AM is best) for a birds eye view of an eruption.  Don't miss the
big multi-color pools in the lower and middle basin areas.  Mid day works
okay here because the colors of the pools are reflected in the steam clouds
above them.  The Norris basin near the west entrance also has a couple of
fairly predictable geysers and lots of features.  Mammouth hot springs is
different every time.  Sometimes there are masses of colorful terraces,
sometimes most of it is just stark white.  Worth a stop.

If you have time, spend a day in the Canyon area and hike down to the
lookouts in the canyon on both sides.  It's part "grand canyon" and part
"Niagra Falls".  The high country near Mt Washburn is good for wildflowers
and high elevation wildlife (e.g. sheep).

If it's open and you have time the Beartooth highway connecting yellowstone
to Red Lodge Montana is one of the more spectacular high altitude roads,
mostly above treeline with great views.  You need a good day for it though
and it's often closed by snow through June or later.

No real suggestions on Rushmore, it's pretty much just go there and shoot
the mountain (if you can see it, one time we gave up after a couple of hours
waiting for fog/clouds to clear.  Jewel Cave and Wind Cave in that area are
also nice if you don't have claustrophobia and want some different natural
scenery.  (Use flash or film or digital cameras that can be corrected for
very yellow light in caves.  I learned that one the hard way)  Devils tower
is also worth looking at and not very far off the interstate.  On the tower
look for people climbing it to add scale to your pictures.

You can't go wrong in the badlands.  Again early and late will have the best
colors.

Mt. Rushmore area, Custer State Park, for Elk, Bighorn Sheep, Pronghorns,
Antelope, mule deer, white tail deer, coyote, buffalo, and begging "feral"
donkeys.  Try needles highway for scenic rock formations, hiking, rock
climbing, etc.  The road up Mt. Coolidge is nice at sunrise or sunset.
Sylvan Lake is picturesque.

Custer State Park borders Wind Cave National Park, the grasslands and
rolling hills above the cave system are nice if you have a high clearance
vehicle to drive the gravel roads.

-mark

Thanks everyone for the helps.
It looks like that we have to go back to drawing board. Since
so much place to visit with so little time, we have decided to
spend the whole week in Teton and Yellowstone.

Mt. Rushmore & Badlands N.P will be some time in future ....