I'm just outside of Durham in hillsborough. Nice small town feel, and plenty of parks and fantastic Greenway, worth looking at if you're moving to the area.
If you're in to baseball, check out the Durham Bulls, they have a really nice ball park with kids area and rooftop bar.
Durham natural science museum is pretty nice too, lots of indoor and outdoor stuff, and catered to kids of all ages.
And there is a really nice, and free to the public, shooting range up in caswell at the game lands. Bout 30 to 40 min or so northwest.
Just a few places to checkout. Welcome to the neighborhood.