We just did the same trip last week, 9 days. Stayed in Lead one night, stopped in Sturgis, Deadwood, Cody, Devils Tower. Yellowstone was very expensive, food @ lodging in West Yellowstone was very high. $135.00 to 225.00. Make sure you look at your rooms before you pay in the 135.00 range.
It rained and or snowed for the first 7 days of our trip. Finally had sunshine thru Jackson, and the last day to Gunnison, CO..
If you go thru Jackson Billys humburgers next door to the Million Dollar bar is cheap and very good.
Hope you have a great trip
Almost forgot you gotta stop at Trevino's Leather shop just south of Deadwood 21412 US Highway 385