A great trail network just a short drive from Spokane.
Riverside State Park is a picturesque, large park and home to the infamous, unidentifiable Bowl & Pitcher (it doesn't look like a Bowl and only vaguely like a pitcher to me). The park is close in to the city (10 miles) yet it is heavily wooded and there are many places to ride. But beware: this park is a family retreat for all the residents of Spokane. You'll find crowds and get scowls from hikers on the north side of the park and equestrians on the south. However, with patience, a smile and a healthy dose of respect for the other denizens of the park, you'll find a good place to work on your skills and meet other cyclists. My best recommendation is to stick close to the river. You'll find some cool single track and some small shale areas which can get pretty technical. To find those areas go right over the suspended bridge. To the left of the suspended bridge you'll find more hills, some fast single track and as you get towards the equestrian stables, some tricky climbs over loose rock.
How to get there:
Ya wimp. Ride in from downtown Spokane, travel towards the river and then south. Go the intersection of Indiana and Division and go west to NW Boulevard. Follow the signs