Going out the northeast entrance on Beartooth hwy. (212) from Cooke City to Red Lodge, there are numerous lakes right along the road. Most have very good fishing and several have campgrounds at the lake. I would suggest Beartooth Lake, Island Lake, and Greenough Lake, but many others are also good. They almost all have good access from the shore.
Someplace along the line, I picked up a map of the Beartooth range that lists all of the lakes and which species of trout can be had in which lake. You can probably find it at the Cooke City General store or at the Top of the World Store on the highway, about 15 east of Cooke City.
As an extra benefit, this road is one of the most spectacular in the country. It hits almost 11,000 feet elevation. It is a curvy mountain road and the grades, while long, are not overly steep. I have had no trouble pulling my 5er across it, but those who are freaked out by mountain driving might do best to avoid it.
Joel