Nik: The Yellowstone river runs through town, there are numerous small streams/creeks in the area and 90 miles SE is the "Big Horn River", one of the great rivers in MT. The NE entrance to Yellowstone NP and the Lamar River and valley is just 130 miles to the SW. Heading SW out of Billings on hwy 212 through Red Lodge, MT leads thru Beartooth Pass and the Beartooth hwy, a beautiful scenic hwy that winds its way along the ridge tops, well worth a saturday drive. If you get the opportunity don't pass up staying at the Pollard Hotel in Red Lodge.
The Pollard Hotel, Red Lodge Montana: Fish Montana and Stay in one of the finest Montana Hotels
Seven miles outside of Red Lodge is a small town called Bearcreek. It has a steakhouse that has fantastic food and offers pig racing during the summer (it is a riot to watch).
Bear Creek Saloon & Steakhouse - Bearcreek, MT
The Big Horn Mountains are just over the border in WY with almost limitless fishing and hunting opportunities.
I don't think you will regret moving to Billings, MT it is a beautiful place and has a lot to offer in the way of fishing and hunting opportunities.
Eric lives in Billings, MT and operates a fly tying shop. He is a member of this forum, user name bighorn flies, you could PM directly or here is his web site contact information if you would rather call:
http://bighornflies.com/Contact.htm
Larry