Couple of options. Join a local club, usually $50, they know ALL the spots and there are a lot of clubs near you. Hit up the local police department, be honest with them. You want to take your little ones on a dirt road, something safe, but give them the feel of adventure. The cops will understand, and will usually point you to something legal and what you are looking for in town or in the area. And another is to find unimproved roads or fire access roads, which I think if you google DEP department of environmental protection ( work with me, iPad here) it may come up with roads around your area.
Btw, many clubs have free forums, you could ask there for dirt roads. Good luck!