Pap, we usually shack up with an old army buddy in Livingston to fish the Yellowstone River between there and Gardiner for a couple days and then head down into the park for a week. We'll fish several spots within the park but I probably like the Firehole most. Went with Wild Trout Outfitters in Big Sky one year down a stretch of the Gallatin River and had a great time.

I don't think there's anywhere in that area where you can't have a great day of fishing -if the trout aren't biting the scenery makes up for it.
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Dwight