People of Wyoming!! Please help

I am traveling from a southern suburb of Minneapolis to Midway, Utah for a wedding over Labor Day weekend. We will have an 8-month old in the car with us. We plan to make it past Rapid City on the first day, then drive the rest of the way on Thursday. Does anyone know if a good area to stay along I-90 in Wyoming? Preferably 2 hours or so away from Rapid City? I don't know the area, and I'm trying to set a travel goal and hotel budget.