There are lots of non-technical trails at Peavine but most if them involve a considerable amount of granny gear climbing. Clear Creek in Jack's Valley (south of Carson City) is less steep and really fun, but further from Reno. If you're coming later in the year the Incline Flume Trail (different from the Flume Trail) is great for beginners.
If you don't mind traveling a bit... like Mahgnillig said, Clear Creek is awesome and the lower sections of Carson City (Ash Canyon) are lots of fun. Other option would be to drive out to Truckee and do Emigrant. Very mellow and flat-ish, nice beginner trail, and then while you are out there hit up the Truckee Bike Park.
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