Billings is, in my experience, arising out of a dozen or so visits, somewhat of a culinary wasteland. All is not lost however.
Enzo's Bistro is very, very good for Mediterranean cooking. I turned some friends onto this place, and they raved about it. Don't miss this place, and please let me know what you think.
If you're not from Montana, you need to go to Pork Chop John's (originally in Butte but now found throughout the state) and order a pork sandwich with everything on it. This is a deep-fried pork patty -- weird but good.
Last, for an old-fashioned roadhouse experience, try the Windmill Club, where you'll get stiff drinks and iceberg salad and decent shrimp (!) and beef served by blue-haired ladies who've probably been working there for decades. The place is always packed.