I haven't driven HWY 2 east from Spokane, but I have from Spokane west to the coast and it is a great highway. Someone else mentioned the Palouse, and it is, indeed, a beautiful highway. I-90 east takes you over several passes and over the Continental Divide.....lot of climbing and descending, but the highway is in good condition, and the views are also spectacular....you'll cross the Clark Fork River many, many times, so you can think of me every time you cross it....
There is a Cabela's in Post Falls, just over the border into Idaho where you could overnight (dry camp) if that is a good stopping point for you....about 30 minutes east of Spokane.