The Gallatin is one of the easier rivers to fly fish in Yellowstone Park. It is relatively shallow in most places and the fish aren't particularly wary. It is composed mostly of riffles and runs which are easily fished with a bushy dry fly such as a Crystal Stimulator or Chernobyl. It is also a good idea to have along a few smaller Muddlers.
Most of the fishable Gallatin is outside the park. The highway to Bozeman provides excellent access for many miles. As the river races toward Bozeman it gains size and some nice fish can be found.
During the stonefly hatch in June be prepared with both dry and wet stonefly patterns.
WOLF AND GREBE LAKES
For the person interested in doing some hiking, these two lakes offer good Grayling fishing in a remote setting. Remember that Grayling is a protected species and return all of them unharmed to the lake. Since there is sometimes bear activity in the backcountry, I'd check with the rangers before hiking in.
THE GARDNER RIVER
Nestled in the northwest portion of Yellowstone, the Gardner doesn't see the angler pressure of the more famous rivers. Most of the fish are small, but occasionally a nicer fish is caught. Most of the water is fast and best fished with a high riding dry fly or a hopper. Since stoneflies are abundant in much of the water, both dry and wet stonefly patterns will be prodive around the time of the hatch. and wet stoneflies thereafter.