You will find small motels & hotels at interchanges all along the highway (assuming you are following I-90 most of the way). Most of these motels will have rooms available for walk ins, unless you are traveling on a major holiday period like Labor Day Weekend. The prices for walk in will be about the same as advance booking.
If you aim for the bigger cities, like Spokane or Coeur d'Alene, then you may find better prices booking in advance for the hotels in town, but not much difference at the highway motel chains.
Once you have decided you have driven enough you could use the big booking sites, like booking.com or hotels.com, to look at nearby hotels to see what they might have. Then either book online or walk in and show the quoted price to the front desk. Most hotels will match the online price if it is lower than their standard walk in price.