Find some events to go to. Pick your interest find an event that caters to it. Billings is big enough that that is almost always something going on. Some fun things that I like to do is Poor Boy Thursdays at Old Chicago, Karaoke at the Red Door on Saturday nights, The Y has basketball every day at noon. So there are tons of things to be done.
You need to do something outdoors if you are living in Montana. Go hunting or fishing or hiking or ANYTHING. You won't realize how great a state it is until you are gone form it. Where else can you throw a line in any body of water and catch a fish. Place is truly magical.
I'm not real familiar with Billings although have spent some time there, usually just a day or two for meetings/conferences or passing through. It's the biggest town in MT, however, so there ought to be social things to do if you look for them. Join a health-club and spend some time there, good for you and you might meet some people. If you're looking for members of the opposite sex to date, try one of the internet dating sites like Match.Com, I suspect you'll find lots of people from the Billings area and while many might think that internet dating smacks of desperation, it's probably better than cruising the bars, plus less expensive and better for your health. I've noticed that Montana towns can be both friendly and cliquish at the same time, so you're probably going to have to be pretty outgoing and think outside the box a little bit in order to make some new friends in the short-term. Good luck.
I find my self with an empty nest and my husband travels alot, so I am not looking for anyone to date - just a girl friend to hang out with, go to dinner, see a movie, shop, go to a ball game, just do stuff. Not sure how or where to find someone in the 50's with similar interests that would want to go have lunch and meet. Just looking for companionship nothing more. Any ideas where or how to find like minded people wanting to just hang out?