txags92 said:
For stream fishing trying to stay outside the park, I would head north up 191 and fish the Gallatin.
Or just as easy to head up a little further west and fish the Madison. For reference, I have not done either but we stay in Big Sky several times a year now and the Gallatin would be a wonderful spot to fish as well.
We head up in a month and staying on the Yellowstone in Paradise Valley down by the river. Plan to do some fishing in that area as well, but that would be more of a hike if starting or staying in West Yellowstone.
Hegben is beautiful as well. We enjoyed some time at the Happy Hour Bar & Grill. If traveling with small children or a convent of nuns, recommend sitting on the patio and paying no attention to the polaroids if one makes a trip to the bathroom.
Again, not a big fisher of fish but the OP may want to check level of rivers if wanting to fish them - August is a bit iffier I believe.