This occurred west of Alkali Station:

Fort Laramie Treaty of 1851, also known as the Horse Creek Treaty: the NPS study of Pony Express Stations mentions Cold Springs Ranch station as the site of the signing of this treaty, citing a letter from Paul Henderson to J.G. Masters, 17 April 1938. This disagrees with another NPS article, part of a web site on Scotts Bluff Monument. Here, the site is said to be where Horse Creek joins the North Platte River.

From Burton:

After satisfying hunger with vile bread and viler coffee—how far from the little forty-berry cup of Egypt!—for which we paid 75 cents, we left Kearney Station without delay. Hugging the right bank of our strange river, at 8 A.M. we found ourselves at Fort Kearney, so called, as is the custom, after the gallant officer, now deceased, of that name.

From Clemens:

A weary drive over a rough and dusty road, through chill night air and clouds of mosquitoes, which we were warned would accompany us to the Pacific slope of the Rocky Mountains, placed us about 10 PM at Rock, also called Turkey Creek --  surely a misnomer, no turkey ever haunted so villainous a spot! Several passengers began to suffer from fever and nausea; in such travel the second night is usually the crisis, after which a man can endure for an indefinite time. The "ranch" was a nice place for invalids, especially for those of the softer sex.

We then stretched once more over the "divide" --  the ground, generally rough or rolling, between the fork or junction of two streams, in fact, the Indian Doab-- separating the Big Blue from its tributary the Little Blue. At 6 PM we changed our fagged animals for fresh, and the land of Kansas for Nebraska, at Cottonwood Creek, a bottom where trees flourished, where the ground had been cleared for corn, and where we detected the prairie wolf watching for the poultry.

July 27. Crossed the Nebraska line about 180 miles from St. Joseph. Here we saw the first Jack Rabbit. They have larger legs bodies, longer legs and longer ears than our rabbits.

This is a clump of board houses on the far side of a shady, well-wooded creek—the Vermilion, a tributary of the Big Blue River, so called from its red sandstone bottom, dotted with granitic and porphyritic boulders.

Resuming, through air refrigerated by rain, our now weary way, we reached at 6 A.M. a favorite camping-ground, the “ Big Nemehaw” Creek, which, like its lesser neighbor, flows after rain into the Missouri River, viâ Turkey Creek, the Big Blue, and the Kansas. It is a fine bottom of rich black soil, whose green woods at that early hour were wet with heavy dew, and scattered over the surface lay pebbles and blocks of quartz and porphyritic granites.

Beyond Kennekuk we crossed the first Grasshopper Creek. Creek, I must warn the English reader, is pronounced “ crik,”and in these lands, as in the jargon of Australia, means not “an arm of the sea,”but a small stream of sweet water, a rivulet; the rivers of Europe, according to the Anglo-American of the West, are “criks.”  On our line there are many grasshopper creeks; they anastomose with, or debouch into, the Kansas River, and they reach the sea viâ the Missouri and the Mississippi.