One of many ways would be to get yourself to Butte, where you can stay in the kitchy motor lodge portion of the Hotel Finlen and eat a myriad of places. From there, take MT 2 over Pipestone Pass to MT 41 to Twin Bridges, where I believe there is a motel. There are also a couple of restaurants Then MT 287 through Sheridan and Virginia City to Ennis, where there is lodging and places to eat. From there, U.S. 287 will take you to U.S. 191, which will take you to W. Yellowstone. IIRC, there is lodging in the Earthquake Lake area.
For a variation from Butte, take I-15 south for a bit and and then its frontage roads to Melrose, where there is a motel and good restaurant. Just south of town, you turn left onto Melrose-Twin Bridges Rd. (a/k/a Melrose Bench Rd.). It's not paved, but it's really cool back there. 20 miles of nothing but some free range cattle. It will take you into Twin Bridges, where you can pick up the route described above.