If you want a park that is beautiful, and really don't like crowds, Dinosaur National Monument in the Utah side is ideal. It is a bit north of Vernal, UT.
There is a small open range road that you drive up. Drive carefully, as we had to stop and wait as a small herd of cattle were in the road, and I had to drive through cattle manure and slow for some deer.
We then took a one mile hike to get to the lookout point for the photo above. We saw one other couple. So a total of two other people in the park. Not much of a crowd.
Then go on over to the Dinosaur National Monument in Colorado. Yes, there are two different Dinosaur National Monuments. The one in Utah has no dinosaurs bones to see, just beautiful scenery. The one in Colorado has a great museum, and the main display is a side of a mountain still with bones in the ground. They have a building built over it. You can touch a real fossil, still in the ground near the end of the tour.
The crowds are typical of popular national parks, but nothing like the Grand Canyon north or south rim.