If you're just aiming for some exercise, you could always go skin up inbounds at Mt Spokane. They have designated uphill routes for the frontside and backside. There's also some decent skinning outside of the resort boundary; you can get about a 2k vert lap if you start at the hairpin turn parking and go to the top.
Otherwise, there aren't a ton options within 30 minutes of Spokane. Depending on snow conditions and where you live, you might be able to poke arounds some of the local hills. For example, people have been known to skin up Mica peak. Some of the regulars on here have other little spots around town, they might chime in.