The greatest national parks in United States

Yellowstone National Park, Wyoming

The geysers, the animals (up close and personal with the buffalo), the waterfalls and Grand Canyon of the Yellowstone.
tips for first time travelers - Go out early in the morning or late in afternoon for the best animal sitings. If you are a hiker get out on the trails. Magic happens in the back country.
Two trails I would reccomend - Fairy Falls and as an overnight - 7 Mile Hole.

Grand Teton National Park

I visit this park several times a year.
Day hikes - Cascade Creek and the Jenny Lake Loop.
If you are camping here go to the rangers talks. You will learn so much about the park.
Visit Jackson Lake Lodge - Be sure to visit the restaurant to see the Carl Roter Murals. They are wonderful

Little Big Horn Battle Field

Even if you don't think you are interested in the Indian Wars and Custer you just might find you will be after this visit.
Tip - Take a tour with Apsalooke Tours. They are run by the community college on the Crow Agency and are led by crow Indians. They are fascinating tours

Gettysburg

Visited in Spring and Fall.
Tip - Hire a docent from the oldest tour association in the US. These guides are Civil War fanatics and they will make you interested in this 3 day battle. They will hop in your car and go out with you in your vehicle and they will also step-on to tour buses.
Visit the new visitors Center.
Have lunch at the Dobbin House.

Grand Canyon, Williams, AZ

It is one thing to see it from the rim To truly experience this canyon you need to get into the canyon. Hike it, Mule ride it or even better take a raft trip down the Colorado.
Tips - It is sandstone stay back from the edges. It takes twice as long to come up as it does to descend. Drink plenty of water and remember that you are at altitude.

Navajo National Monument

This place is magic. You need to hike down switchbacks, 1000 ft. on a ranger guided tour of the Betatakin Ruins. If you have the time and the energy hike the 8 miles in to the Keet Seel Ruins. They are some of the most complete pre-Puebloan (Anazazi) ruins left in the Desert Southwest.

Mesa Verde

Plan to spend some time here. Go on the ranger guided tours. Be somewhere on the rim where you can be safe during a Thunderstorm.
Crosscountry ski in the winter - there is hardly anyone there.