Or, if you're not in a hurry to return to Pullman, and the weather is good and you don't mind your car getting a little dusty, try taking the old Pullman-Moscow Highway. About half of it is gravel, but generally well maintained. It offers spectacular views of the Palouse.
To get there, go past the Kibbie Dome parking lot south on Perimeter Drive, and take a sharp right onto the road marked "Old Pullman Highway" (in Pullman it's called the "Old Moscow Highway," naturally).