A monument on Cavanal Mountain near Poteau, Oklahoma is labeled as follows:
"WORLD'S HIGHEST HILL"
ELEVATION: 1,999 FT.
Here's a photo taken by the author:
The marking of 1,999 feet is curious, because the actual elevation as shown on the Poteau West USGS 7-1/2 minute quadrangle is 2385.
Presumably the highest hill claim is based on classifying any summit of 2000 feet or greater as a mountain. Hence, a hill of 1999 feet would be as high as it could be and still be counted, because a mere 1 foot higher would make it a mountain. Fair enough, but Cavanal Mountain juts up 385 feet beyond that. By this criterion, I suggest the following hills as contenders for the highest hill. These are some United States summits that come up to just under 2000 feet. No doubt, there are similar summits in other countries.
Nail Factory Mountain in Pennsylvania, 1999 feet
Little Chemise Knob in California, 1999 feet
Another way to classify summits would be by topographic prominence. Perhaps the folks that placed a monument on Cavanal Mountain had that in mind. But Cavanal's prominence comes up a bit short at 1795 feet. Marys Mountain in Nevada has a prominence of 1999 feet.
I think it's more fun to just take summits as they are named. That is, if it is named as a hill, then count it as a hill. Here is a list of the highest named hills that I found in each state down to Oklahoma:
My nomination for the highest hill in the United States is Bull Hill in Colorado, near Mount Elbert. I have been to the top of Cavanal Mountain, but not Bull Hill. The view from Cavanal Mountain is fine. You can look down on Poteau and over at Sugar Loaf, which is Oklahoma's most prominent. I can't speak for Bull Hill, but I anticipate that the view from there is fine, too.