Well, there's the Spokane Falls (see
Riverfront Park Official Website). I would imagine there's plenty of spots along the Spokane River outside of the city as well. Lake Couer d'Alene I'm sure has beach parks too.
If you have time and a car there's the option of driving south towards Pullman and getting into the Palouse (wheat country, rolling hills sculpted by ancient floods from Glacial Lake Missoula). Pretty country down there!
Or head west out into the Channeled Scablands region (see
Channeled Scablands - Wikipedia, the free encyclopedia). Grand Coulee Dam is only a couple of hours drive from Spokane (90 miles), Moses Lake and the Potholes only a little further drive. Seeing the dry coulees is pretty impressive (especially when you see a canyon half a mile across and 300-400 feet deep and realize it was ripped out of the basalt bedrock by floods in just a couple of weeks as the glacial floods roared across the Columbia Plateau in the last ice age...
Drive east on I-90 thru the old mining town of Kellog, you can get some cool shots of the freeway construction as it goes thru tha canyon there (wish I had done that stop on my trips...).
Hope that helps give ya some options. Pretty cool place to visit, I've always thought.
Jim