"Green River, he said, was a good town"
green river map
GNU Free Documentation Licensegreen river map - Credit: Seth IIys
Map showing the location of Green River, Wyoming.

Although Dunn does not specify which Green River the Binewskis plan to leave their child in, (there are several) Judging by the mountains she desribes on their journey and its position west of Laramie, where Al has sent the rest of the carnival east to, it would be a reasonable assumption that she is referring to Green River, Wyoming.