I guess I should toss in a couple other suggestions along Highway 20, in case you have the time.
Red Rock RV Park on the south side of Henry's Lake isn't a bad spot for a base camp. Besides a view of Henry's Lake and ready access to its fishing, the park affords day trips up Sawtelle Peak Rd (zig-zag gravel, toad-only), at the top of which is a nearly 360 degree view of some big country. A large satellite/air traffic/security dome installation is up there, but I still managed to get a complete circle of photos to stitch into a glorious panorama. There was also a regular "rodeo"/BBQ of sorts just up the street from the RV park, put on by a local ranch I think. Sandhill Cranes nest across the road from the park and provide local entertainment. You can also take a day's toad drive up over Red Rock Pass toward Red Rock Lakes, and take in some nice backcountry; a small creek crosses that road that some consider the headwaters of the Missouri. RV park staff will gladly supply more info.
Not far south from there, north of Mack's Inn, is the road east to Big Springs, and you don't want to miss that. The road loops back west to exit near Mack's Inn as I recall. Further south is Last Chance aka Island Park, the last town of any size before West Yellowstone. More flyshops there usually get my business and supply me with updated information. There's a nice RV area at the Northeast end of Island Park Reservoir, and I can't remember whether it is National Forest, State, or County run, but it was pretty large and nice, certainly not crowded and we parked for several days just off the water, with handy docks to walk out on and fish from. Forest fires were bad that year, and I got some great photos of uniquely colored sunsets across the lake. This year is ramping up to be another bad fire season, so keep that in mind - you may get into a lot of smoke while travelling the West.
If you stay at either place, or one of the other parks around Last Chance and Mack's Inn, you can take a day in the toad and drive the Highway 87, along Henry's Lake's north shore, up to Highway 287 that fronts the Madison River, and loop east along Quake Lake that way, follow along Hebgen Lake to 191 south into West Yellowstone, then hit 20 west back toward your start; or take the route in reverse, but the clockwise loop gets you into W. Yellowstone for an afternoon or evening meal at one of the many restaurants and fast food places, or to get groceries to take back to camp. You could also take a short jaunt west of the 87/287 junction and go south to check out Wade and Cliff Lakes, one of which at least at one time held the Montana State Brown Trout record, and may still. A cruise Northwest up 287 will garner some super views of the great Madison River Valley - typical Big Sky impressions on your soul (especially if you flyfish
).
Joel
Below are pix of the Willow Creek fire affect at sunset, off a dock at Island Park Reservoir, and from the middle of the Buffalo River looking up Elk Creek, where hatching mayflies reflect the flash of my camera.