I've moved away from the area, but people have been mentioning a lot of the places that I used to go. Private timber is pretty well locked down in your area, so the public places are your main option.
For hiking around, my favorites are the forest service off 410 past Federation Forest and Capitol Forest. The Greenwater Lakes trail is nice and easy for the first couple miles if you want to let the little ones walk a little. I've never done any hiking in Tiger Mountain up north, but I've hunting there and I think there's a good trail system there too.
For hunting, all these areas have a reputation for being extremely crowded. I've hunted in or nearby all these areas many times without seeing another person. You'll run into people when you get back to the road, but if you're off the road you're by yourself.