Where can I find train routes using Wild West locomotives?

The type of 8-wheel steam locomotive in most of your pictures is know as the 4-4-0, also known as the American. 4-4-0 only describes the wheel pattern, not design features like the conical chimney (to catch sparks on wood-burning locomotives) and the large cowcatcher. Still, this configuration was most popular in the U.S. from the 1860s to the 1880s, which correspond roughly to the years of the Wild West, and many of the locomotives manufactured in that period would have sported such features.

Unfortunately for you, all the surviving specimens from that era are in museums, like the General and the Dayton. Steam locomotives have been retired from regular duty even in India, so I highly doubt you would be able to find one for a regular long-distance ride, especially of this older design.

There are replicas, however. The Leviathan 63 travels around the Midwestern United States. Earlier this year you could pay for a 15-mile round trip from the Indiana Transportation Museum in Noblesville. Another option is the William H. Simpson #17, a replica of the train that took President Lincoln to Gettysburg, based in York County, Pennsylvania. If you happen to be at Walt Disney World in Florida, the No. 4 Roy O. Disney, a 1916 4-4-0, still operates on the Walt Disney World Railroad.

There are also a number of mid-20th century replicas in operation at various zoos, theme parks, and museums, like the #7 Robert E. Lee at the Historic Jefferson Railway, the Omaha Zoo Railroad 119, and 4-4-0 No. 1 The Oregon at the Washington Park and Zoo Railway in Portland (closed for renovations). They are steam locomotives with the design features you seem to be interested in, but are not authentic to the period, typically using oil-fired engines (more efficient and less environmentally damaging to operate).