The most common reason Pullmanites head for Spokane is probably the airport, which provides far better connections at lower cost than the Pullman-Moscow airport, even if you factor in an overnight stay in a budget motel to get its free parking privileges during a longer trip. (If you work for the university, be sure to ask about state employee discounts.)
People also go to see medical specialists, shop, or attend entertainments. You're more likely to catch unusual movies in Pullman or Moscow than you are in Spokane, but touring companies of Broadway shows regularly pass through the Opera House, along with other popular entertainments (but not often opera). The Spokane Symphony and Chorale perform here regularly.