The west end of Billings has a Dog Park over by the baseball fields! 

"Centennial Dog Park in Billings, MT, is pet-friendly. After walking on the trails in the surrounding park and watching locals play baseball and softball on the many fields, let Fido play his own ball games safe inside this fenced dog park. The park is divided into a large dog and small dog section, so that all pups can play safely and freely. Centennial Dog Park is open every day of the week from dawn until dusk. " -BringFido.com

If you're located in the heights, the High Sierra Dog Park is a great option! 

"High Sierra is Billings first official dog park. Located in the heights behind the water tower across from the church and Skyview High School. This park has 14 developed acres with 7.5 of them being use for the High Sierra Dog Park. There is a fenced in area for small dogs as well. Call (406) 657-8371 for questions about the park. " -BringFido.com