Chaea90---
I accessed the Historic Dallas Morning News through the Dallas Public Library database list. I searched for "railways" and "fares," and "[name of railway]" and "fares." (Not using quote marks.) I got about 50 advertisements per search, most with excursion fares to specific cities.
Then I went to Portal to Texas History to do a Guided Search using the same terms. More than 9,000 hits made the results unusable. (The was due to all the newspaper responses, each newspaper in the collection carrying the same ad during the same week.) I bet if I had fiddled around with Portal a little more, I could have sharpened the results or found route maps (listing fares) in their collection.
Depending on how deep you need to go, this should get you started.