If you are looking for fun family days out in the October half-term the best answer is a day at the races. Horse racing in October should be top of the list when looking for things to do in Stockton or what's on in the surrounding areas. This race day at Sedgefield is one of the most prestigious meetings of the year and features the iconic Durham National. A fixture at Sedgefield since 1955, The Durham National is the biggest race to take place at the racecourse. The race happens every October and is run over three and three-quarter miles.