My first choice would be to do Devil's Tower. Devil's Tower is 1267 feet above the Belle Fourche River in Crook County, Wyoming. Devil's Tower was declared the first national monument by President Theodore Roosevelt. It is believed to have been the last standing parts of an old volcano. Throughout the years it has been eroding slightly, but every year their are about 400,000 visitors that take the challenge to climb to the top.
My second choice is the Craters of the Moon. it is located in the Snake River Plain in Idaho. It has an elevation of around 5,900 feet above sea level. The monument was established on May 2, 1924. It covers an area of 1,117 square miles of three major lava fields and 400 square miles of sagebrush steppe grasslands. It ususally gets around 200,000 visitors each year.
My third choice is Crazy Horse. It is in Black Hills, South Dakota. The monument is getting carved into Thunderhead Mountain and it is still under construction. When it is finsihed it is believed to be 641 feet wide and 563 feet high. It has been under construction since 1948. When the monument will be finished, it is going to be the world's largest sculpture.