I'm just north of downtown Woodstock off of Main St. And I certainly sympathize! Riding around here is tough. All the roads seem busy. On weekend mornings (when there's less traffic) sometimes I ride a loop consisting of Dupree, Bascomb Carmel, Bells Ferry, Ridge, Sixes, and Hwy 5. But even during "low" traffic there's still a lot of traffic on at least half of those roads. Toonigh Road seems to be a bit less busy, and someone I know over that way says Univeter and Butterworth are ridable (but I've never tried them). But it really seems you can't put a decent route together without getting on a busy road.
Outspokin bike shop (in downtown Woodstock) does Saturday morning rides that leave out of the Hickory Flat Publix (on Hwy 140) and go to the east from there. Traffic over there seems lighter and the cars we do encounter are a bit more used to seeing bikes on the road since lots of folks ride over there every weekend. This would be roads like Lower Union Hill, Union Hill, Arbor Hill, Trinity Church, Gaddis, Gantt and Sugar Pike. But of course that means racking up the bike and driving somewhere which is always a pain. I have another riding buddy that lives in Towne Lake and he says for his weekday rides he just stays in his neighborhood. As a consequence he is getting really good at hill climbing!