Start at the Mary Laveroni Park. There is ample parking space here. Go down past the skate park and over a wooden bridge to get access to the trails. From here you have an assortment of options to start riding short fun trails right in town. This trail is the old Hetch Hetchy Railroad grade that is now grown over. There are some obstacles in the trail that you need to watch out for and it is not very well maintained.
It could be a great place to ride right in town if a little work was put into cleaning up the old railroad grade. Trail goes to Deer Flat road where you can cross to continue going to Wards Ferry road. There is a great viewpoint of the Tuolumne Canyon right before Deer Flat road.