Several sophisticated chains are represented, like Williams-Sonoma and Nordstrom. The parking garage at the center is handy, but expensive. Drive past RiverPark Square two or three blocks east and you can often find cheap or free on-street parking.
Why is there no RiverPark Square Web site listing the businesses there?
If you're willing to make the trek east on I-5 a few miles, there is lots more shopping with free parking at the Spokane Valley Mall.