I live at the foot of Mt. Diablo. The mountain trail is built for cars, but used almost exclusively by cyclists. It's a cycling mecca. In fact the surrounding area (Walnut Creek) offers a myriad of street and paved path cycling in great weather. With a great downtown to start or end your ride, simply riding the Iron Horse Trail is something to consider.
If you are not a beginner, and/or are looking for more of a challenging one and not a simple trail I would suggest Mission Peak in Fremont ( it is near Ohlone College off of Mission) When I hike it I see a lot of bikers, but BEWARE. It is not for the faint of heart :)