The Oregon Trail in Wyoming is 491 miles long. The half way point of the trip was at Independence Rock.
It depended on a lot of factors when the travelers would arrive in Wyoming. Early July was supposed to be best, but if things got held up, any time in July would do. The problem would be if they got into Wyoming later. The nights would start getting cold. There would be less daylight. They could run into trouble in the mountain region toward the end of the trail.
The temperature in July in Wyoming would hover around 95 degrees F. It could get hotter than that and the nights would only cool down a bit.
By now, the families would have a solid routine. They would know the others they wanted to avoid. They knew some that they would probably know for the rest of their lives.
South Wyoming is an interesting place if you are a tourist. They weren’t tourists and a lot of the high desert would have lost its charm in the heat and dust.

One thing to keep in mind is that Wyoming and Nebraska were territories and the borders were different.

The maps.

Oregon Trail Map  by, National Park Service

NASA Topographical Map with the Oregon Trail drawn by Matthew Trump, Wikipedia Commons.

Map showing the prairie grasses by US Department of agriculture. I put the asterisk on Wyoming.

Next is a modern county map of Wyoming by R. Blauert, Wikipedia Commons. I put in first letters of the major landmarks seen on the trail.

F is for Fort Laramie was a private trading post.
R is the most eastern landmark. It stands for Register Cliff. This area is where the wagon ruts are now seen by tourists.
I is for Independence Rock, It is also the half way point on the trail.
S is for the Sweetwater River and South Pass. They crossed the Continental Divide at South Pass.
G is for Green River. They crossed this river.

This is a county map of Wyoming  by, G. Blauert, Wikipedia Commons. I put the initials on it.
This is a map of the North Platte River by, background, DEMIS Mapserver and the rivers are drawn by Shannon1, Wikipedia Commons.
The trail followed this river and other rivers because they needed water. There was also grassland for the animals.

This is a modern picture of the North Platte River by, Wussel007, Wikipedia Commons.

This is a modern road map by, National Park Service and it shows a part of Wyoming and the locations of Fort Laramie and Independence Rock.
These next two pictures are paintings of Fort Laramie  from memory by Alfred Jacob Miller, 1810-1874. It was located between the Platte and Laramie Rivers.
The first is before 1840. The second is the interior of the fort in 1840. The fort changed ownership a few times in the 1840s.

This picture of the fort was taken around 1868, photographer unknown.

And a picture from modern times. Photo by, Phil Nickell, Wikipedia Commons.

This picture is an old one of Register Cliff. Photographer unknown. Some travelers scratched their names on the cliff.

This is a picture of Register Cliff by, National Park Service.

This is a National Park Service map of a part of Wyoming where wagon ruts from the Oregon Trail are located.

The next three pictures of of these wagon ruts by, National Park Service.

Next is a picture of a wagon train by, National Park Service.

This is a map of Sweetwater River and Green River. The Sweetwater River is a tributary of the North Platte River.

The next pictures are of Independence Rock.

This picture is of Devils Gate at Sweetwater River  by, National Park Service.

This is Independence Rock on the Sweetwater River  by, Department of the Interior General Land Office, US Geological Survey Territories. It was taken in 1870. It is 130 feet high and 1,900 feet long. Some travelers put their names on this rock.

This is a picture of the same area taken by William Henry Jackson, 1843-1942. I’m not sure when the photo was taken.

Another picture of Independence Rock by, National Park Service.

This is a picture of the trail at Sweetwater River  by, the Interior Department General Land Office, US Geological Survey, Territories. It was taken in 1870.

This is the marker for Oregon Trail at South Pass. It is taken by, Randy C. Bunney, Great Circle Photographics.

A picture taken  of the Oregon Trail at South Pass  by, National Park Service.

The last picture is of Green River  by, US Geological Survey.