I loved Olympic National Park. We visited it in late August and found it was not crowded at all, the wildflowers were in bloom and the weather was perfect. This park has it all: mountains, rain forests, beautiful coastline. It's worth the time to see all aspects of it.
There are many, many beautiful National Parks and Monuments in the U.S. The number of people at each park will depend on the time of year visited. Many of the parks are even more beautiful and enjoyable during the off season. Visit the Grand Canyon in the winter for clearer weather and fewer people. If you are lucky enough to be there when it snows, the canyon looks frosted and is exceptionally beautiful. Yellowstone National Park is so incredible that it's worth putting up with some crowds just to see it. In Utah, visit Arches, Bryce and Canyonlands in the spring or fall for smaller crowds.
It is impossible to choose "the best" National Park; they are all so beautiful!