You should consider Tribble Mill Park. It sounds like exactly what you are looking for.
It's not in the Norcross area, but if you work in Norcross the commute would not be difficult from this area.
There are many great opportunities to buy a home in the Lawrenceville/Grayson area that would be convienent to the park.
I've included a link for you to review some information on the park. If you are interested in searching for homes in this area be sure to contact me. I would be glad to help.
ERA Sunrise Realty