There can be great fishing along the whole stretch of the Gallatin right up throw YC. Usually not the size but great action...BE CAREFUL driving on that road at all times of the day. If it is like it usually is during the summer you would think you are in L.A. oh wait....you basically are.
You can make the loop down to Earth Quake Lake head up to the Ennis Area (straight west of BigSky). If you have kids Virginia City is kind of a neat place to stop. You could stop and fish the Madison a little. You could go to Bozeman for some shopping and the Museum of the Rockies otherwise I avoid it like the plague. It was probably my favorite place to be until about 2014. You could also head north to Four Corners then shoot west and hit the Madison River in that area...also a pretty cool Buffalo Jump historical area up there.