Have you considered a vacation which highlights science: the flora (plants), fauna (animals), and geology of an area. You will find many interesting and family friendly sites in South Dakota and Wyoming.
The Badlands National Park, part of the National Park System (NPS), has the world's richest Oligocene fossil beds. They are 37 to 28 million years old. It is also one of the largest mixed-grass prairies in the United States. Before you enter the Badlands, be certain you have fuel, water, and snacks. Your best chance for photographs will be either at sunset or sunrise, but just in case buy some post cards. It is very difficult to capture the array of colors.
Wall Drug is an experience not to be missed. You will find a very nice rock shop and bookstore as well as South Dakota made souvenirs, Black Hills gold, pottery, and Native American artifacts. Be sure to read about how this phenomenon got its start and have either a bison steak or bison burger while you are here.
Mount Rushmore National Memorial (NPS) has the images of George Washington, Thomas Jefferson, Theodore Roosevelt, and Abraham Lincoln. Scientists have estimated the rate of erosion at 1 inch per 10,000 years. Be sure to visit the artist's studio on site where you will see a model of the carving at 1/12th scale. One inch on the model became one foot on the mountain.
In nearby Keystone, you can visit the Gutzon Borglum Museum and see more of the artist's work. You will see a copy of Lincoln's eye, the same size as it appears on the mountain. Did you know that a sister of Laura Ingalls Wilder once lived in Keystone?
Take a drive through the Needles area of the Black Hills National Forest. If you look carefully, you can see Mount Rushmore off in the distance.
Crazy Horse Memorial, in Custer, was started in 1948 by Korczak Ziolkowski after a request from Lakota Chief Henry Standing Bear. Korczak died in 1982, but he left behind detailed instructions so that his family has been able to continue his work. At the site, you can also see the sculptor's log home studio and workshop as well as the Indian Museum of North America.
There are many caves in the Black Hills area. My favorite is Jewel Cave National Monument, part of the National Park System (NPS). At 141 miles, it is the second longest cave system in the world. It has lots of calcite crystals and delicate strands of gypsum.
Wind Cave National Park (NPS) at 126 miles is the 4th longest cave in the world. In 1903, President Theodore Roosevelt designated this cave as the first in the nation to become a National Park. It is best known for its boxwork, thin calcite fins that resemble honey combs. The 28,295 acre mixed-grass prairie is home to elk, pronghorn, mule deer, coyotes, prairie dogs, and bison. PLEASE DO NOT APPROACH THE ANIMALS TO PHOTOGRAPH THEM. STAY IN YOUR VEHICLE. Bison are very bad-tempered animals, especially the males. Also, please do not feed the animals. Prairie dogs have a very nasty bite and junk food is not healthy for them.
The Custer State Park covers 71,000 acres and has one of the nation's largest bison herds. Several scenes from the movie "Dances with Wolves" were filmed here.
South of Custer, in Hot Springs, you will find the Mammoth Dig Site. It has the world's largest collection of mammoths with 55 Columbian mammoths and woolly mammoths as well. This is an excellent paleotological site for Pleistocene study. The site was discovered when digging began on a housing development. After some bones were unearthed, scientists were consulted. As you walk through the site you can watch individuals at work uncovering more fossils.
Bear Country USA, near Rapid City, is a 250 acre drive through wildlife park with200 animals representing 25 species including: black bears, grizzlies, bison, wolves, elk, and big horn sheep.
Reptile Gardens, near Rapid City, has a wonderful collection of reptiles as well as many extraordinary plants. Be sure to see the giant tortoises and Komodo dragons.
Be certain to visit the Museum of Geology at the South Dakota School of Mines and Technology in Rapid City to learn more about the geology of this area. By the way, you will find many rock shops in western South Dakota.
The final scene of the movie "Dances with Wolves" was shot in Spearfish Canyon. It is a beautiful area and best known for fly-fishing.
Be sure to visit the Cleghorn Fish Hatchery which raises rainbow trout.
The opening scene of the movie "Dances with Wolves" had the Indians camped along the river on the flats near Belle Fourche.
Devil's Tower was designated by President Theodore Roosevelt in 1906 as the nation's first National Monument (NPS). This igneous intrusion into the sedimentary rock rises 1267 feet above the Belle Fourche River. It did not become visible until water erosion removed the sedimentary rock. The phonolite porphyry is light to dark gray to greenish-gray igneous rock with conspicuous crystals of white feldspar which as it cooled formed hexagonal as well as 4,5, and 7 sided columns. The site covers 1347 acres. Be sure to read about the Indians' legends relating to this site.
Yellowstone National Park (NPS) has more than 300 geysers, two thirds of those on Earth, as well as hot springs, mudpots, and steaming fumaroles. Old Faithful may be the best known, but there are many others to see.
You may wish to check the National Park Service website as well as South Dakotat and Wyoming Tourism sites.