'Parkruns' are a free weekly 5km timed run. There are no parkruns in Billingham but there are a few within a 10-15min drive. View full details on the parkrun webpages (which includes a map of the route):

Parkrun Address website
Hartlepool Maritime Avenue, Hartlepool, TS24 0XF Website
Sedgefield Hardwick Park - Hardwick Park Visitors' Centre Website
Tees Barrage Tees Barrage International White Water Centre, TS18 2QW. Website
Albert Park Albert Park, Middlesbrough Website
Stewart Park Outside Captain Cook Museum Website